Hosoya Polynomial of Hierarchical Product of Graphs

The Hosoya polynomial of a graph G is a graphical invariant polynomial that its first derivative at x = 1 is equal to the Wiener index. In this paper we compute the Hosoya polynomial of the hierarchical product of graphs and give some applications of this operation.

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

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

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

[4]  Heping Zhang,et al.  Hosoya polynomials under gated amalgamations , 2008, Discret. Appl. Math..

[5]  Lali Barrière,et al.  The generalized hierarchical product of graphs , 2009, Discret. Math..

[6]  Dragan Stevanovic,et al.  Hosoya polynomial of composite graphs , 2001, Discret. Math..

[7]  Miss A.O. Penney.  (b) , 1974, The New Yale Book of Quotations.

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

[9]  Bijan Taeri,et al.  Four new sums of graphs and their Wiener indices , 2009, Discret. Appl. Math..

[10]  M. Diudea,et al.  The Wiener Polynomial Derivatives and Other Topological Indices in Chemical Research , 2000 .

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

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

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

[14]  Dennis H. Rouvray,et al.  The Rich Legacy of Half a Century of the Wiener Index , 2002 .

[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..