Computing Szeged Index of Certain Nanosheets Using Partition Technique

Distance properties of molecular graphs form an important topic in chemical graph theory. The Szeged index is a molecular structure descriptor equal to the sum of products neu(e|G) · nev(e|G) over all edges e =( uv) of the molecular graph G, where neu(e|G )i s the number of vertices whose distance to vertexu is smaller than the distance to vertex v ,a nd wherenev(e|G) is defined analogously. In this paper we compute the Szeged index of certain chemical graphs without using distance matrix.

[1]  Ali Reza Ashrafi,et al.  Vertex and edge PI indices of Cartesian product graphs , 2008, Discret. Appl. Math..

[2]  I. Gutman,et al.  Mathematical Concepts in Organic Chemistry , 1986 .

[3]  B. Mohar,et al.  How to compute the Wiener index of a graph , 1988 .

[4]  Bharati Rajan,et al.  Embedding of hypercubes into necklace, windmill and snake graphs , 2012, Inf. Process. Lett..

[5]  Janez Žerovnik COMPUTING THE SZEGED INDEX , 1996 .

[6]  Andrey A. Dobrynin,et al.  The Szeged Index and an Analogy with the Wiener Index , 1995, J. Chem. Inf. Comput. Sci..

[7]  Sandi Klavzar,et al.  An Algorithm for the Calculation of the Szeged Index of Benzenoid Hydrocarbons , 1995, J. Chem. Inf. Comput. Sci..

[8]  I. Gutman,et al.  Wiener Index of Trees: Theory and Applications , 2001 .

[9]  Victor Chepoi,et al.  The Wiener Index and the Szeged Index of Benzenoid Systems in Linear Time , 1997, J. Chem. Inf. Comput. Sci..

[10]  P. Manuel,et al.  A New Technique to Compute Padmakar-Ivan Index and Szeged Index of Pericondensed Benzenoid Graphs , 2014 .

[11]  Gerd Wechsung,et al.  Embedding ladders and caterpillars into the hypercube , 1998, Discret. Appl. Math..

[12]  Ernesto Estrada,et al.  Chemical Graph Theory , 2013 .

[13]  I. Gutman,et al.  The Edge Version of the Szeged Index , 2008 .

[14]  Sandi Klavÿzar A BIRD'S EYE VIEW OF THE CUT METHOD AND A SURVEY OF ITS APPLICATIONS IN CHEMICAL GRAPH THEORY , 2008 .

[15]  Albert William,et al.  Embedding of cycles and wheels into arbitrary trees , 2004, Networks.

[16]  Peter E. John,et al.  A Method of Computing the PI Index of Benzenoid Hydrocarbons Using Orthogonal Cuts , 2007 .

[17]  Bharati Rajan,et al.  A New Approach to Compute Wiener Index , 2013 .

[18]  István Lukovits,et al.  Szeged Index - Applications for Drug Modeling&# , 2005 .

[19]  I. Gutman,et al.  Wiener Index of Hexagonal Systems , 2002 .

[20]  Sandi Klavžar,et al.  The Szeged and the Wiener Index of Graphs , 1996 .