{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,2]],"date-time":"2024-08-02T11:16:08Z","timestamp":1722597368627},"reference-count":78,"publisher":"Elsevier BV","content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Information Sciences"],"published-print":{"date-parts":[[2014,9]]},"DOI":"10.1016\/j.ins.2014.03.133","type":"journal-article","created":{"date-parts":[[2014,4,25]],"date-time":"2014-04-25T09:31:48Z","timestamp":1398418308000},"page":"22-33","update-policy":"http:\/\/dx.doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":143,"special_numbering":"C","title":["Extremality of degree-based graph entropies"],"prefix":"10.1016","volume":"278","author":[{"given":"Shujuan","family":"Cao","sequence":"first","affiliation":[]},{"given":"Matthias","family":"Dehmer","sequence":"additional","affiliation":[]},{"given":"Yongtang","family":"Shi","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.ins.2014.03.133_b0005","first-page":"R64","article-title":"Sum of squares of degrees in a graph","volume":"10","author":"\u00c0brego","year":"2009","journal-title":"J. Inequal. Pure Appl. Math."},{"key":"10.1016\/j.ins.2014.03.133_b0010","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/BF01902206","article-title":"Graphs with maximal number of adjacent pairs of edges","volume":"32","author":"Ahlswede","year":"1978","journal-title":"Acta Math. Acad. Sci. Hungar."},{"key":"10.1016\/j.ins.2014.03.133_b0015","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1016\/0009-2614(82)80009-2","article-title":"Distance connectivity index","volume":"89","author":"Balaban","year":"1982","journal-title":"Chem. Phys. Lett."},{"key":"10.1016\/j.ins.2014.03.133_b0020","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1016\/j.dam.2007.09.008","article-title":"On the variance of Shannon products of graphs","volume":"156","author":"Balogh","year":"2008","journal-title":"Discrete Appl. Math."},{"key":"10.1016\/j.ins.2014.03.133_b0025","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/S0012-365X(98)00195-2","article-title":"Two path extremal graphs and an application to a Ramsey-type problem","volume":"196","author":"Byer","year":"1999","journal-title":"Discrete Math."},{"key":"10.1016\/j.ins.2014.03.133_b0030","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/S0012-365X(03)00130-4","article-title":"An upper bound on the sum of squares of degrees in a hypergraph","volume":"269","author":"Bey","year":"2003","journal-title":"Discrete Math."},{"key":"10.1016\/j.ins.2014.03.133_b0035","series-title":"Extremal Graph Theory","author":"Bollob\u00e1s","year":"1978"},{"key":"10.1016\/j.ins.2014.03.133_b0040","first-page":"225","article-title":"Graphs of extremal weights","volume":"50","author":"Bollob\u00e1s","year":"1998","journal-title":"Ars Combin."},{"key":"10.1016\/j.ins.2014.03.133_b0045","doi-asserted-by":"crossref","first-page":"R42","DOI":"10.37236\/1795","article-title":"Degree powers in graphs with forbidden subgraphs","volume":"11","author":"Bollob\u00e1s","year":"2004","journal-title":"Electron. J. Comb."},{"key":"10.1016\/j.ins.2014.03.133_b0050","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1017\/S0963548311000654","article-title":"Degree powers in graphs: the Erd\u00f6s-Stone theorem","volume":"21","author":"Bollob\u00e1s","year":"2012","journal-title":"Comb. Probab. Comput."},{"key":"10.1016\/j.ins.2014.03.133_b0055","series-title":"Information Theoretic Indices for Characterization of Chemical Structures","author":"Bonchev","year":"1983"},{"key":"10.1016\/j.ins.2014.03.133_b0060","series-title":"Chemical Graph Theory: Introduction and Fundamentals","author":"Bonchev","year":"1991"},{"key":"10.1016\/j.ins.2014.03.133_b0065","doi-asserted-by":"crossref","first-page":"4517","DOI":"10.1063\/1.434593","article-title":"Information theory, distance matrix and molecular branching","volume":"67","author":"Bonchev","year":"1977","journal-title":"J. Chem. Phy."},{"key":"10.1016\/j.ins.2014.03.133_b0070","series-title":"Graph Theory","author":"Bondy","year":"2008"},{"key":"10.1016\/j.ins.2014.03.133_b0075","first-page":"151","article-title":"Graphs with large variance","volume":"57","author":"Caro","year":"2000","journal-title":"Ars Combin."},{"key":"10.1016\/j.ins.2014.03.133_b0080","doi-asserted-by":"crossref","first-page":"R47","DOI":"10.37236\/1525","article-title":"A Tur\u00e1n type problem concerning the powers of the degrees of a graph","volume":"7","author":"Caro","year":"2000","journal-title":"Electron. J. Comb."},{"key":"10.1016\/j.ins.2014.03.133_b0085","doi-asserted-by":"crossref","first-page":"1959","DOI":"10.1016\/j.disc.2006.03.054","article-title":"Sums of powers of the degrees of a graph","volume":"306","author":"Cioab\u0103","year":"2006","journal-title":"Discrete Math."},{"key":"10.1016\/j.ins.2014.03.133_b0090","series-title":"Elements of Information Theory","author":"Cover","year":"2006"},{"key":"10.1016\/j.ins.2014.03.133_b0095","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/S0012-365X(97)00213-6","article-title":"An upper bound on the sum of squares of degrees in a graph","volume":"185","author":"de Caen","year":"1998","journal-title":"Discrete Math."},{"key":"10.1016\/j.ins.2014.03.133_b0100","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1016\/j.amc.2007.12.010","article-title":"Information processing in complex networks: graph entropy and information functionals","volume":"201","author":"Dehmer","year":"2008","journal-title":"Appl. Math. Comput."},{"issue":"2","key":"10.1016\/j.ins.2014.03.133_b0105","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.compbiolchem.2007.09.007","article-title":"Structural information content of networks: graph entropy based on local vertex functionals","volume":"32","author":"Dehmer","year":"2008","journal-title":"Comput. Biol. Chem."},{"issue":"8","key":"10.1016\/j.ins.2014.03.133_b0110","doi-asserted-by":"crossref","first-page":"e3079","DOI":"10.1371\/journal.pone.0003079","article-title":"Entropy bounds for molecular hierarchical networks","volume":"3","author":"Dehmer","year":"2008","journal-title":"PLoS ONE"},{"key":"10.1016\/j.ins.2014.03.133_b0115","first-page":"889","article-title":"On extremal properties of graph entropies","volume":"68","author":"Dehmer","year":"2012","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"10.1016\/j.ins.2014.03.133_b0120","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.ins.2010.08.041","article-title":"A history of graph entropy measures","volume":"181","author":"Dehmer","year":"2011","journal-title":"Inform. Sci."},{"key":"10.1016\/j.ins.2014.03.133_b0125","series-title":"Advances in Network Complexity","author":"Dehmer","year":"2013"},{"key":"10.1016\/j.ins.2014.03.133_b0130","doi-asserted-by":"crossref","first-page":"1655","DOI":"10.1021\/ci900060x","article-title":"On entropy-based molecular descriptors: statistical analysis of real and synthetic chemical structures","volume":"49","author":"Dehmer","year":"2009","journal-title":"J. Chem. Inf. Model."},{"key":"10.1016\/j.ins.2014.03.133_b0135","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1023\/A:1010767517079","article-title":"Wiener index of trees: theory and applications","volume":"66","author":"Dobrynin","year":"2001","journal-title":"Acta Appl. Math."},{"key":"10.1016\/j.ins.2014.03.133_b0140","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/S0893-9659(97)00028-1","article-title":"Some bounds on entropy measures in information theory","volume":"10","author":"Dragomir","year":"1997","journal-title":"Appl. Math. Lett."},{"key":"10.1016\/j.ins.2014.03.133_b0145","doi-asserted-by":"crossref","first-page":"e34523","DOI":"10.1371\/journal.pone.0034523","article-title":"Exploring statistical and population aspects of network complexity","volume":"7","author":"Emmert-Streib","year":"2012","journal-title":"PLoS ONE"},{"key":"10.1016\/j.ins.2014.03.133_b0150","unstructured":"P. Erd\u00f6s, MR505076 Review of [2] Math. Reviews 80g:05053 (1978)."},{"key":"10.1016\/j.ins.2014.03.133_b0155","first-page":"249","article-title":"On the graph theorem of Tur\u00e1n","volume":"21","author":"Erd\u00f6s","year":"1970","journal-title":"Matematikai Lapok"},{"key":"10.1016\/j.ins.2014.03.133_b0160","doi-asserted-by":"crossref","first-page":"2613","DOI":"10.1016\/j.disc.2008.03.025","article-title":"Number of walks and degree powers in a graph","volume":"309","author":"Fiol","year":"2009","journal-title":"Discrete Math."},{"key":"10.1016\/j.ins.2014.03.133_b0165","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1002\/jgt.20119","article-title":"Moments of graphs in monotone families","volume":"51","author":"F\u00fcredi","year":"2006","journal-title":"J. Graph Theory"},{"key":"10.1016\/j.ins.2014.03.133_b0170","series-title":"Algebraic Graph Theory","author":"Godsil","year":"2001"},{"key":"10.1016\/j.ins.2014.03.133_b0175","doi-asserted-by":"crossref","first-page":"778","DOI":"10.2307\/2310464","article-title":"On sets of acquaintances and strangers at any party","volume":"66","author":"Goodman","year":"1959","journal-title":"Amer. Math. Monthly"},{"key":"10.1016\/j.ins.2014.03.133_b0180","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1017\/S1446788700022199","article-title":"Triangles in a complete chromatic graph","volume":"39","author":"Goodman","year":"1985","journal-title":"J. Austral. Math. Soc. (Ser. A)"},{"key":"10.1016\/j.ins.2014.03.133_b0185","unstructured":"R. Gu, X. Li, Y. Shi, Degree powers in C5-free graphs, Bull. Malays. Math. Sci. Soc. in press."},{"key":"10.1016\/j.ins.2014.03.133_b0190","first-page":"1","article-title":"The energy of a graph","volume":"103","author":"Gutman","year":"1978","journal-title":"Ber. Math.\u2013Statist. Sekt. Forschungsz. Graz"},{"key":"10.1016\/j.ins.2014.03.133_b0195","doi-asserted-by":"crossref","first-page":"1087","DOI":"10.1021\/ci00021a009","article-title":"Selected properties of the Schultz molecular topological index","volume":"34","author":"Gutman","year":"1994","journal-title":"J. Chem. Inf. Comput. Sci."},{"key":"10.1016\/j.ins.2014.03.133_b0200","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/S0065-3276(06)51003-2","article-title":"Chemical graph theory\u2014the mathematical connection","volume":"51","author":"Gutman","year":"2006","journal-title":"Adv. Quantum Chem."},{"key":"10.1016\/j.ins.2014.03.133_b0205","series-title":"Analysis of Complex Networks: From Biology to Linguistics","first-page":"145","article-title":"Graph energy","author":"Gutman","year":"2009"},{"key":"10.1016\/j.ins.2014.03.133_b0210","first-page":"30","article-title":"The variance of the vertex degrees of randomly generated graphs","volume":"13","author":"Gutman","year":"2002","journal-title":"Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat."},{"key":"10.1016\/j.ins.2014.03.133_b0215","series-title":"Inequalities","author":"Hardy","year":"1988"},{"key":"10.1016\/j.ins.2014.03.133_b0220","doi-asserted-by":"crossref","first-page":"2332","DOI":"10.1246\/bcsj.44.2332","article-title":"Topological index: a newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons","volume":"44","author":"Hosoya","year":"1971","journal-title":"Bull. Chem. Soc. Jpn."},{"key":"10.1016\/j.ins.2014.03.133_b0225","doi-asserted-by":"crossref","first-page":"1044","DOI":"10.1016\/j.dam.2006.11.008","article-title":"Connected (n,m)-graphs with minimum and maximum zeroth-order general Randi\u0107 index","volume":"155","author":"Hu","year":"2007","journal-title":"Discrete Appl. Math."},{"key":"10.1016\/j.ins.2014.03.133_b0230","first-page":"425","article-title":"On molecular graphs with smallest and greatest zeroth-order general Randi\u0107 index","volume":"54","author":"Hu","year":"2005","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"10.1016\/j.ins.2014.03.133_b0235","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1002\/jgt.10025","article-title":"Minimizer graphs for a class of extremal problems","volume":"39","author":"Ismailescu","year":"2002","journal-title":"J. Graph Theory"},{"key":"10.1016\/j.ins.2014.03.133_b0240","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1007\/BF02771620","article-title":"Rearrangements of (0\u20131) matrices","volume":"9","author":"Katz","year":"1971","journal-title":"Israel J. Math."},{"key":"10.1016\/j.ins.2014.03.133_b0245","series-title":"Molecular Connectivity in Chemistry and Drug Research","author":"Kier","year":"1976"},{"key":"10.1016\/j.ins.2014.03.133_b0250","series-title":"Molecular Connectivity in Structure\u2013Activity Analysis","author":"Kier","year":"1986"},{"key":"10.1016\/j.ins.2014.03.133_b0255","first-page":"371","article-title":"The meaning of molecular connectivity: a bimolecular accessibility model","volume":"75","author":"Kier","year":"2002","journal-title":"Croat. Chem. Acta"},{"key":"10.1016\/j.ins.2014.03.133_b0260","unstructured":"J. K\u00f6rner, Coding of an information source having ambiguous alphabet and the entropy of graphs, in: Transactions of the 6-th Prague Conference on Information Theory, 1973, pp. 411\u2013425."},{"key":"10.1016\/j.ins.2014.03.133_b0265","unstructured":"X. Li, I. Gutman, Mathematical Aspects of Randi\u0107-Type Molecular Structure Descriptors, Mathematical Chemistry Monographs No.1, Kragujevac, 2006."},{"key":"10.1016\/j.ins.2014.03.133_b0270","first-page":"127","article-title":"A survey on the Randi\u0107 index","volume":"59","author":"Li","year":"2008","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"10.1016\/j.ins.2014.03.133_b0275","series-title":"Graph Energy","author":"Li","year":"2012"},{"key":"10.1016\/j.ins.2014.03.133_b0280","first-page":"57","article-title":"Trees with the first three smallest and largest generalized topological indices","volume":"50","author":"Li","year":"2004","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"10.1016\/j.ins.2014.03.133_b0285","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1007\/s003730200041","article-title":"An extremal problem on degree sequences of graphs","volume":"18","author":"Linial","year":"2002","journal-title":"Graphs Combin."},{"key":"10.1016\/j.ins.2014.03.133_b0290","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1007\/BF02476948","article-title":"Entropy and the complexity of the graphs I: an index of the relative complexity of a graph","volume":"30","author":"Mowshowitz","year":"1968","journal-title":"Bull. Math. Biophys."},{"key":"10.1016\/j.ins.2014.03.133_b0295","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1007\/BF02476692","article-title":"Entropy and the complexity of graphs II: the information content of digraphs and infinite graphs","volume":"30","author":"Mowshowitz","year":"1968","journal-title":"Bull. Math. Biophys."},{"key":"10.1016\/j.ins.2014.03.133_b0300","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1007\/BF02476603","article-title":"Entropy and the complexity of graphs III: graphs with prescribed information content","volume":"30","author":"Mowshowitz","year":"1968","journal-title":"Bull. Math. Biophys."},{"key":"10.1016\/j.ins.2014.03.133_b0305","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1007\/BF02476673","article-title":"Entropy and the complexity of graphs IV: entropy measures and graphical structure","volume":"30","author":"Mowshowitz","year":"1968","journal-title":"Bull. Math. Biophys."},{"key":"10.1016\/j.ins.2014.03.133_b0310","doi-asserted-by":"crossref","first-page":"R107","DOI":"10.37236\/196","article-title":"Degree powers in graphs with a forbidden even cycle","volume":"16","author":"Nikiforov","year":"2009","journal-title":"Electron. J. Comb."},{"key":"10.1016\/j.ins.2014.03.133_b0315","first-page":"267","article-title":"A conjecture of Goodman and the multiplicities of graphs","volume":"14","author":"Olpp","year":"1996","journal-title":"Australasian J. Combin."},{"key":"10.1016\/j.ins.2014.03.133_b0320","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1002\/(SICI)1097-0118(199908)31:4<283::AID-JGT3>3.0.CO;2-H","article-title":"(n,e)-Graphs with maximum sum of squares of degrees","volume":"31","author":"Peled","year":"1999","journal-title":"J. Graph Theory"},{"key":"10.1016\/j.ins.2014.03.133_b0325","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/0378-8733(81)90014-9","article-title":"The degree variance: an index of graph heterogeneity","volume":"3","author":"Snijders","year":"1981","journal-title":"Social Netw."},{"key":"10.1016\/j.ins.2014.03.133_b0330","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/978-3-540-44485-5_9","article-title":"Information theory of complex networks: on evolution and architectural constraints","volume":"650","author":"Sol","year":"2004","journal-title":"Complex Netw. Lect. Notes Phys."},{"key":"10.1016\/j.ins.2014.03.133_b0335","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1007\/BF02477860","article-title":"Life, information theory, and topology","volume":"17","author":"Rashevsky","year":"1955","journal-title":"Bull. Math. Biophys."},{"key":"10.1016\/j.ins.2014.03.133_b0340","doi-asserted-by":"crossref","first-page":"6609","DOI":"10.1021\/ja00856a001","article-title":"On characterization of molecular branching","volume":"97","author":"Randi\u0107","year":"1975","journal-title":"J. Am. Chem. Soc."},{"key":"10.1016\/j.ins.2014.03.133_b0345","first-page":"5","article-title":"On history of the Randi\u0107 index and emerging hostility toward chemical graph theory","volume":"59","author":"Randi\u0107","year":"2008","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"10.1016\/j.ins.2014.03.133_b0350","series-title":"The Mathematical Theory of Communication","author":"Shannon","year":"1949"},{"key":"10.1016\/j.ins.2014.03.133_b0355","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/S0020-0190(01)00191-0","article-title":"Entropy lower bounds for quantum decision tree complexity","volume":"81","author":"Shi","year":"2002","journal-title":"Inf. Process. Lett."},{"key":"10.1016\/j.ins.2014.03.133_b0360","unstructured":"B. Sudakov, Recent developments in extremal combinatorics: Ramsey and turn type problems, in: Proceedings of the International Congress of Mathematicians, vol. IV, 2010, pp. 2579\u20132606."},{"key":"10.1016\/j.ins.2014.03.133_b0365","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/0012-365X(92)90321-6","article-title":"An inequality for degree sequences","volume":"103","author":"Sz\u00e9kely","year":"1992","journal-title":"Discrete Math."},{"key":"10.1016\/j.ins.2014.03.133_b0370","first-page":"1","article-title":"Network structure entropy and its application to scale-free networks","volume":"6","author":"Tan","year":"2004","journal-title":"Syst. Eng.-Theory Pract."},{"key":"10.1016\/j.ins.2014.03.133_b0375","series-title":"Handbook of Molecular Descriptors","author":"Todeschini","year":"2002"},{"key":"10.1016\/j.ins.2014.03.133_b0380","first-page":"129","article-title":"A note on the information content of graphs","volume":"18","author":"Trucco","year":"1965","journal-title":"Bull. Math. Biol."},{"key":"10.1016\/j.ins.2014.03.133_b0385","series-title":"Chemical Graph Theory","author":"Trinajstic","year":"1992"},{"key":"10.1016\/j.ins.2014.03.133_b0390","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1021\/ja01193a005","article-title":"Structural determination of paraffin boiling points","volume":"69","author":"Wiener","year":"1947","journal-title":"J. Am. Chem. Soc."}],"container-title":["Information Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0020025514004393?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0020025514004393?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2020,8,18]],"date-time":"2020-08-18T06:45:55Z","timestamp":1597733155000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0020025514004393"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,9]]},"references-count":78,"alternative-id":["S0020025514004393"],"URL":"https:\/\/doi.org\/10.1016\/j.ins.2014.03.133","relation":{},"ISSN":["0020-0255"],"issn-type":[{"value":"0020-0255","type":"print"}],"subject":[],"published":{"date-parts":[[2014,9]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Extremality of degree-based graph entropies","name":"articletitle","label":"Article Title"},{"value":"Information Sciences","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.ins.2014.03.133","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"Copyright \u00a9 2014 Elsevier Inc. All rights reserved.","name":"copyright","label":"Copyright"}]}}