Vertex-Weighted Wiener Polynomials for Composite Graphs

Recently introduced vertex-weighted Wiener polynomials are a generalization of both vertex-weighted Wiener numbers and ordinary Wiener polynomials. We present here explicit formulae for vertex-weighted Wiener polynomials of the most frequently encountered classes of composite graphs.

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

[2]  István Lukovits,et al.  On the Definition of the Hyper-Wiener Index for Cycle-Containing Structures , 1995, J. Chem. Inf. Comput. Sci..

[3]  N. Trinajstic,et al.  The Zagreb Indices 30 Years After , 2003 .

[4]  István Lukovits,et al.  Extensions of the Wiener Number , 1996, J. Chem. Inf. Comput. Sci..

[5]  Danail Bonchev,et al.  Vertex-weightings for distance moments and thorny graphs , 2007, Discret. Appl. Math..

[6]  I. Gutman,et al.  Some recent results in the theory of the Wiener number , 1993 .

[7]  Y. Yeh,et al.  A Crowning Moment for Wiener Indices , 2004 .

[8]  N. Zefirov,et al.  Combinatorial models and algorithms in chemistry. The expanded Wiener number—a novel topological index , 1990 .

[9]  Haruo Hosoya,et al.  On some counting polynomials in chemistry , 1988, Discret. Appl. Math..

[10]  H. Wiener.  Relation of the physical properties of the isomeric alkanes to molecular structure; surface, tension, specific dispersion, and critical solution temperature in aniline. , 1948, The Journal of physical and colloid chemistry.

[11]  Alexandru T. Balaban,et al.  Topological indices based on topological distances in molecular graphs , 1983 .

[12]  Yeong-Nan Yeh,et al.  The Wiener polynomial of a graph , 1996 .

[13]  Douglas J. Klein,et al.  Building-block Computation of Wiener-type Indices for the Virtual Screening of Combinatorial Libraries* , 2002 .

[14]  Douglas J. Klein,et al.  Wiener-Number-Related Sequences , 1999, J. Chem. Inf. Comput. Sci..

[15]  M. Randic.  Novel molecular descriptor for structure—property studies , 1993 .

[16]  Ivan Gutman,et al.  On the sum of all distances in composite graphs , 1994, Discret. Math..

[17]  Ernesto Estrada,et al.  Generalization of topological indices , 2001 .

[18]  H. Wiener.  Structural determination of paraffin boiling points. , 1947, Journal of the American Chemical Society.

[19]  Bo-Yin Yang,et al.  The behavior of Wiener indices and polynomials of graphs under five graph decorations , 2007, Appl. Math. Lett..