Properties of commuting graphs over semidihedral groups

Abstract

<p>This paper considers commuting graphs over the semidihedral group SD<sub>8n</sub> . We compute their eigenvalues and obtain that these commuting graphs are not hyperenergetic for odd n ≥ 15 or even n ≥ 2. We further compute the Laplacian spectrum, the Laplacian energy and the number of spanning trees of the commuting graphs over SD<sub>8n</sub> . We also discuss vertex connectivity, planarity, and minimum disconnecting sets of these graphs and prove that these commuting graphs are not Hamiltonian.</p>