Path-positive graphs

Bapat, R. B. ; Lal, A. K. (1991) Path-positive graphs Linear Algebra and its Applications, 149 . pp. 125-149. ISSN 0024-3795

Full text not available from this repository.

Official URL:

Related URL:


For any positive integer k let Pk denote the characteristic polynomial of the adjacency matrix of the path on k vertices. We obtain certain results regarding Pk evaluated at A(G), the adjacency matrix of any given graph G. For some special graphs G, we describe the matrix Pk(A(G)) completely. We call a graph G path-positive if Pk(A(G)) is a nonnegative matrix for all positive integers k. It is shown that if G is a connected graph with a vertex of degree at least four, then G is path-positive. We conjecture that all connected graphs are path-positive apart from a few exceptional cases described in the paper.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
ID Code:78315
Deposited On:19 Jan 2012 06:31
Last Modified:19 Jan 2012 06:31

Repository Staff Only: item control page