Line graph characterization of the order supergraph of a finite group

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Document Type : Original paper

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Department of Mathematics, Birla Institute of Technology and Science Pilani, Pilani-333031, India

Abstract

The power graph ${\mathcal{P}(G)}$ is the simple undirected graph with group elements as a vertex set and two elements are adjacent if one of them is a power of the other. The order supergraph ${\mathcal{S}(G)}$ of the power graph ${\mathcal{P}(G)}$ is the simple undirected graph with vertex set $G$ in which two vertices $x$ and $y$ are adjacent if $o(x)\vert o(y)$ or $o(y)\vert o(x)$. In this paper, we classify all the finite groups $G$ such that the order supergraph ${\mathcal{S}(G)}$ is the line graph of some graph. Moreover, we characterize finite groups whose order supergraphs are the complement of line graphs.

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References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 21 August 2024

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