On The Commuting Graph of Semidihedral Group

2020/08/17 by Kumar, Jitender, Dalal, Sandeep, Baghel, Vedant
#05C25 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2008.07098

Abstract

The commuting graph Δ(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 Δ(G), we investigate Δ(SD_8n) the commuting graph of the semidihedral group SD_8n. In this connection, we discuss various graph invariants of Δ(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 Δ(SD_8n).

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