A note on the entropy of graphs

Document Type: Original Article

Author

Department of Mathematics, Shahid Rajaee Teacher Training University

Abstract

A useful tool for investigation various problems in mathematical chemistry and  computational physics is graph entropy.  In this paper, we introduce a new version of graph entropy  and  then we determine it for some classes of graphs.

Graphical Abstract

A note on the entropy of graphs

Keywords


[1] L. W. Beineke, R. Wilson and P. J. Cameron, Topics in Algebraic Graph Theory, New York: Cambridge University Press, 2004.

[2] M. Dehmer, F. Emmert-Streib and Y. Shi, Interrelations of graph distance measures based on topological indices, PLoS ONE 9 (2014) e94985.

[3] M. Dehmer, F. Emmert-Streib and Y. Shi, Graph distance measures based on topological indices revisited, Appl. Math. Comput. 266 (2015) 623–633.

[4] M. Dehmer and A. Mehler, A new method of measuring similarity for a special class of directed graphs, Tatra Mt. Math. Publ. 36 (2007) 39–59.

[5] M. Dehmer and A. Mowshowitz, Generalized graph entropies, Complexity 17 (2011) 45–50.

[6] M. Dehmer, A. Mowshowitz and F. Emmert-Streib, Connections between classical and parametric network entropies PLoS One 6 (2011) e15733.

[7] M. Dehmer, L. Sivakumar and K. Varmuza, Uniquely discriminating molecular structures using novel eigenvalue-based descriptors. MATCH Commun. Math. Comput. Chem. 67 (2012) 147–172.

[8] M. Dehmer, Strukturelle Analyse web-basierter Dokumente, in: Multimedia und Telekooperation, Deutscher Universit¨ats Verlag,Wiesbaden, 2006.

[9] M. Dehmer, K. Varmuza, S. Borgert and F. Emmert-Streib, On entropy-based molecular descriptors: Statistical analysis of real and synthetic chemical structures, J. Chem. Inf. Model. 49 (2009) 1655-1663.

[10] C. E. Shannon andW.Weaver, The Mathematical Theory of Communication; University of Illinois Press, Urbana, IL, USA, 1949.