On The Commuting Graph of Semidihedral Group

Abstract

The commuting graph $\Delta (G)$ of a finite non-abelian group $G$ is a simple graph with vertex set $G$ and two distinct vertices $x,y$ are adjacent if $xy=yx$. In this paper, among some properties of $\Delta (G)$, we investigate $\Delta (S{D}_{8n})$ the commuting graph of the semidihedral group $S{D}_{8n}$. In this connection, we discuss various graph invariants of $\Delta (S{D}_{8n})$ including minimum degree, vertex connectivity, independence number, matching number and detour properties. We also obtain the Laplacian spectrum, metric dimension and resolving polynomial of $\Delta (S{D}_{8n})$.