Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques Vol. CXXXI, No. 30, pp. 1–7 (2005) 

Some relations between distance–based polynomials of treesI. GutmanFaculty of Science, University of Kragujevac, P. O. Box 60, 34000 Kragujevac, Serbia and MontenegroAbstract: 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 distancebased 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 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 21 Nov 2005. This page was last modified: 20 Jun 2011.
© 2005 Mathematical Institute of the Serbian Academy of Science and Arts
