Laplacian polynomial of square power graph of dihedral group of order 2n with even natural number n

Abstract

Square power graph of the dihedral group D_n of order 2n, Γ_sq (D_n) is a simple undirected finite graph with vertex set D_n having pairs of different vertices u,v adjacent iff uv=w^2 or vu=w^2 for any w∈D_n with w^2≠e where e is the identity element of D_n. In this research work we have calculated laplacian polynomial of Γ_sq (D_n) when n is even natural number.