HOSOYA POLYNOMIAL OF THORN TREES, RODS, RINGS, AND STARS

The Hosoya polynomial is determined for thorn trees, thorn rods, rings, and stars, which are special cases of thorn graphs. By this some earlier results by Bonchev and Klein are generalized. Various distance{based topological indices, namely Wiener index, hyper{Wiener index, Harary index, and reciprocal Wiener index can thus be computed for the classes of graphs under consideration.

[1]  Yeong-Nan Yeh,et al.  The Wiener polynomial of a graph , 1998, math/9801011.

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

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

[4]  Zlatko Mihalić,et al.  A graph-theoretical approach to structure-property relationships , 1992 .

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

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

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

[8]  Ivan Gutman,et al.  Graph representation of organic molecules Cayley's plerograms vs. his kenograms , 1998 .

[9]  I. Gutman Relation between hyper-Wiener and Wiener index , 2002 .

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

[11]  Sandi Klavzar,et al.  WIENER-TYPE INVARIANTS OF TREES AND THEIR RELATION , 2004 .

[12]  Boris Furtula,et al.  Hyper-Wiener Index vs. Wiener Index. Two Highly Correlated Structure-Descriptors , 2003 .

[13]  Frank Harary,et al.  The number of caterpillars , 1973, Discret. Math..

[14]  S. El-Basil Applications of caterpillar trees in chemistry and physics , 1987 .

[15]  Ovidiu Ivanciuc,et al.  Design of topological indices. Part 4. Reciprocal distance matrix, related local vertex invariants and topological indices , 1993 .

[16]  Nenad Trinajstić,et al.  Harary Index - Twelve Years Later* , 2002 .

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

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

[19]  P. Hansen,et al.  Trees with Palindromic Hosoya Polynomials , 1999 .

[20]  Aleksander Vesel,et al.  Wiener-type topological indices of phenylenes , 2002 .

[21]  Mircea V. Diudea,et al.  Indices of Reciprocal Properties or Harary Indices , 1997, J. Chem. Inf. Comput. Sci..

[22]  N. Trinajstic,et al.  On the Harary index for the characterization of chemical graphs , 1993 .

[23]  Ivan Gutman,et al.  A Collective Property of Trees and Chemical Trees , 1998, J. Chem. Inf. Comput. Sci..

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

[25]  D. Klein,et al.  On the wiener number of thorn trees, stars, rings, and rods , 2002 .

[26]  Gordon G. Cash,et al.  Three Methods for Calculation of the Hyper-Wiener Index of Molecular Graphs , 2002, J. Chem. Inf. Comput. Sci..