Inverse graphs associated with finite groups

Monther Rashed Alfuraidan, Yusuf F. Zakariya


Let $(\Gamma,*)$ be a finite group and $S$ a possibly empty subset of $\Gamma$ containing its non-self-invertible elements. In this paper, we introduce the inverse graph associated with $\Gamma$ whose set of vertices coincides with $\Gamma$ such that two distinct vertices $u$ and $v$ are adjacent if and only if either $u * v\in S$ or $v * u\in S$. We then investigate its algebraic and combinatorial structures.


finite group, inverse graph, non-self-invertible, planar graphs, Hamiltonian graphs

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ISSN: 2338-2287

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