Order sum signed graph of a group

Document Type : Research Paper

Authors

Department of Mathematics, Christ University, Bangalore, India

Abstract

The order sum graph associated with the group $G$, denoted by $\Gamma_{os}$, is a graph with vertex set consisting of elements of $G$ and two vertices say $a$,$b$ $\in \Gamma_{os}$ are adjacent if $o(a)+o(b)>o(G)$, where $o(\ast)$ denotes the order of a group or an element of a group. In this paper, we introduce a signed graph called order sum signed graph where the underlying graph is a complete graph of order $n$ and the edges receive positive and negative signs based on the order sum graph. We characterise the balanced negated order sum signed graphs. We also characterise the positive and negative homogeneous order sum signed graphs. Further, we study the properties such as clusterability, sign-compatibility, consistency and switching of signed graphs. Further, we obtain the adjacency spectra, Laplacian spectra and signless Laplacian spectra of the order sum signed graphs associated with cyclic groups.

Keywords

References

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Journal of Algebra and Related Topics
Volume 12, Issue 2
January 2025
Pages 87-98

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