On Distance Induced Seidel Matrices for Signed Graphs

Articles in Press

Document Type : Original paper

Authors

1 Department of Mathematics, P R N S S College, Mattannur, Kannur, Kerala, India

2 Research Scholar, Dr. Hermann Gundert Central Library and Research Centre, Kannur University, Kerala, India

3 Principal(Retired), Government Arts and Science College, Uduma, Kasaragod 671318

Abstract

A signed graph Σ=(G,σ) is a graph G together with a signature function σ which assigns 1 or −1 on the edges of G. Seidel matrix of an unsigned graph is already defined and researchers investigated some of its spectral and other properties. Considering the recently introduced notion of signed distance in signed graphs and that of the distance compatible signed graphs, we define distance induced Seidel matrices for such signed graphs and analyze their spectrum mainly for some classes of unbalanced distance compatible signed graphs, as balanced signed graphs possess the same distance induced Seidel spectrum as that of its underlying graph. We also deal with the distance compatibility issue in the line graph of a distance compatible signed graph and discuss the corresponding distance induced Seidel spectrum in this regard.

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 08 July 2025

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