PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Terminal polynomials and star-like graphs
Boris Horvat, Tomaž Pisanski and Milan Randić
MATCH Commun. Math. Comput. Chem. Volume 60, Number 2, pp. 493-512, 2008. ISSN 0340-6253

Abstract

A terminal polynomial is the characteristic polynomial of the distance matrix between all pairs of leaves (valence one vertices) of a given graph. Two graphs are isoterminal if they share the same terminal polynomial. In this paper we prove the Clarke-type theorem about terminal polynomial of a given graph and prove that there are countably many isoterminal pairs of graphs. We investigate isoterminal pairs of star-like graphs in more details and calculate the isoterminal pair of star-like graphs with three rays that has the smallest number of vertices (in both graphs together) compared to all isoterminal pairs of star-like graphs with three rays.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:8162
Deposited By:Boris Horvat
Deposited On:21 February 2012