On Stress of a Vertex in a Graph

K. Bhargava; N. N. Dattatreya; R. Rajendra

On Stress of a Vertex in a Graph

Combinatorics 2023-10-04 v3

Authors: K. Bhargava , N. N. Dattatreya , R. Rajendra

Abstract

The stress of a vertex in a graph is the number of geodesics passing through it (A. Shimbel, 1953). A graph is $k$ -stress regular if stress of each of its vertices is $k$ . In this paper, we investigate some results and compute stress of vertices in some standard graphs and give a characterization of graphs with all vertices of zero stress except for one. Also we compute stress of vertices in graphs of diameter 2 and in the corona product $K_m \circ G$ . Further we prove that any strongly regular graph is stress regular and characterize $k$ -stress regular graphs for $k=0,1,2$ .

Keywords

graph stress geodesic stress regular graph strongly regular graph corona product graph diameter

Cite

@article{arxiv.2208.13493,
  title  = {On Stress of a Vertex in a Graph},
  author = {K. Bhargava and N. N. Dattatreya and R. Rajendra},
  journal= {arXiv preprint arXiv:2208.13493},
  year   = {2023}
}

Comments

11 pages, 12 figures. Due to some unavoidable reasons, paper could not be published in Palestine Journal of Mathematics. No other changes in the content

On Stress of a Vertex in a Graph

Abstract

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