On the complement of the intersection graph of subgroups of a group

Document Type : Original paper

Authors

1 Department of Mathematics, Sri Paramakalyani College, Alwarkurichi - 627 412, Tamil Nadu, India.

2 Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram - 624 302, Tamil Nadu, India

Abstract

The complement of the intersection graph of subgroups of a group $G$, denoted by $\mathcal{I}^c(G)$, is the graph whose vertex set is the set of all nontrivial proper subgroups of $G$ and its two distinct vertices $H$ and $K$ are adjacent if and only if $H\cap K$ is trivial. In this paper, we classify all finite groups whose complement of the intersection graph of subgroups is one of totally disconnected, bipartite, complete bipartite, tree, star graph or $C_3$-free. Also we characterize all the finite groups whose complement of the intersection graph of subgroups is planar.

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References

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Communications in Combinatorics and Optimization
Volume 10, Issue 1
March 2025
Pages 57-68

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