Inverse graphs associated with finite groups

Monther Rashed Alfuraidan (Department of Mathematics & Statistics King Fahd University of Petroleum and Minerals Dhahran 31261, Saudi Arabia)
Yusuf F. Zakariya (Departments of Science Education Ahmadu Bello University Zaria, Nigeria)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 5, No 1 (2017): Electronic Journal of Graph Theory and Applications

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.