Randić index and information

Abstract The Randic index R G is one of the classical graph-based molecular structure descriptors that found countless applications in chemistry and pharmacology. The mathematical background of this index is also well elaborated. We now point out a hitherto unnoticed feature of R G , namely its connection with the degree-based information content of a (molecular) graph. This connection is based on the linear correlation between R G and the logarithm of the multiplicative version of the Randic index.

[1]  M. Randic.  Characterization of molecular branching , 1975 .

[2]  Béla Bollobás,et al.  Graphs of Extremal Weights , 1998, Ars Comb..

[3]  Xueliang Li,et al.  A Survey on the Randic Index , 2008 .

[4]  Wolfgang Linert,et al.  The Multiplicative Version of the Wiener Index , 2000, J. Chem. Inf. Comput. Sci..

[5]  Shaun M. Fallat,et al.  On the normalized Laplacian energy and general Randić index R-1 of graphs , 2010 .

[6]  Béla Bollobás,et al.  Extremal graphs for weights , 1999, Discret. Math..

[7]  M. Randic,et al.  The connectivity index 25 years after. , 2001, Journal of molecular graphics & modelling.

[8]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[9]  On the Multiplicative Wiener Index and Its Possible Chemical Applications , 2000 .

[10]  Kinkar Chandra Das,et al.  On Wiener and multiplicative Wiener indices of graphs , 2016, Discret. Appl. Math..

[11]  L. Hall,et al.  Molecular connectivity in chemistry and drug research , 1976 .

[12]  Jean-Loup Faulon,et al.  OMG: Open Molecule Generator , 2012, Journal of Cheminformatics.

[13]  Chris Morley,et al.  Open Babel: An open chemical toolbox , 2011, J. Cheminformatics.

[14]  Claude E. Shannon,et al.  The mathematical theory of communication , 1950 .

[15]  R. Todeschini,et al.  Molecular Descriptors for Chemoinformatics: Volume I: Alphabetical Listing / Volume II: Appendices, References , 2009 .

[16]  Ramin Kazemi.  Note on the multiplicative Zagreb indices , 2016, Discret. Appl. Math..

[17]  Consonni,et al.  New Local Vertex Invariants and Molecular Descriptors Based on Functions of the Vertex Degrees , 2010 .

[18]  R. Kazemi.  On the Multiplicative Zagreb Indices of Bucket Recursive Trees , 2017 .

[19]  Ordering of trees by multiplicative second Zagreb index , 2016 .

[20]  I. Gutman.  Degree-Based Topological Indices , 2013 .