Vertex Stress Polynomial of a Graph

Prajna S Rai; Rajendra R; P. Siva Kota Reddy

doi:10.5269/bspm.68311

Authors

Prajna S Rai JSS Science and Technology University
Rajendra R Department of mathematics, Mangalore unviersity, Mangalagangothti-574199
P. Siva Kota Reddy JSS Science and Technology University

DOI:

https://doi.org/10.5269/bspm.68311

Abstract

The notion of stress of a vertex in a graph was introduced by Alfonso Shimbel in 1953. The stress of a vertex in a graph is the number of shortest paths passing through that vertex. In this paper, we introduce the concept of vertex stress polynomial of a graph and obtain some results including a characterization of graphs with vertex stress polynomial a non-zero constant.