  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
$\Delta(SD_{8n})$ the commuting graph of the semidihedral group $SD_{8n}$. In
this connection, we discuss various graph invariants of $\Delta(SD_{8n})$
including minimum degree, vertex connectivity, independence number, matching
number and detour properties. We also obtain the Laplacian spectrum, metric
dimension and resolving polynomial of $\Delta(SD_{8n})$.
