Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques   EMIS ELibM Electronic Journals Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
Académie Serbe des Sciences et des Arts, Beograd

Vol. CXXXI, No. 30, pp. 1-7 (2005)

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Some relations between distance--based polynomials of trees

I. Gutman

Faculty of Science, University of Kragujevac, P. O. Box 60, 34000 Kragujevac, Serbia and Montenegro

Abstract: The Hosoya polynomial $H(G,\lambda)$ of a graph $G$ has the property that its first derivative at $\lambda=1$ is equal to the Wiener index. Sometime ago two distance-based graph invariants were studied -- the Schultz index $S$ and its modification $S^\ast$\,. We construct distance--based graph polynomials $H_1(G,\lambda)$ and $H_2(G,\lambda)$\,, such that their first derivatives at $\lambda=1$ are, respectively, equal to $S$ and $S^\ast$\,. In case of trees, $H_1(G,\lambda)$ and $H_2(G,\lambda)$ are related with $H(G,\lambda)$\,.

Keywords: Graph polynomial, distance (in graph), tree, Wiener index, Schultz index

Classification (MSC2000): 05C12, 05C05

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Electronic version published on: 11 Apr 2006. This page was last modified: 13 Apr 2006.

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