Eigenvalues of Adjacency and Laplacian Matrices of Bracelet—Kn Graph

Abstract

Let G be an undirected simple graph. Adjacency matrix of a graph G, denoted by (A(G)), is defined as a matrix which has entry-(i, j) is equal 1 if vertex i and vertex j are adjacent and 0 if otherwise. Let D(G) be the diagonal matrix of vertex degree and J(G) be the matrix which has entry all ones. Laplacian matrix (L(G)) can be defined by L(G) = D(G) – A(G). This study discusses eigenvalues of adjacency and Laplacian matrices of the Bracelet—Kn graph. The results of this study indicate that the Bracelet—Kn graph for n ≥ 4, n even has four different eigenvalues of adjacency and Laplacian matrices.