Fidyatus Safitri, Purwanto Purwanto, Santi Irawati
Research on the algebraic graph theory is still being developed by many researchers. Let Z be a commutative ring. A graph I( Z) is a graph with a vertex set of units Z and x, y? Z, x?y, are adjacent if and only if x. y=1, and all vertices adjacent to 1. The complement of I( Z)= (V(I( Z)), E(I( Z))), denoted by I( Z)¯=(V(I( Z))¯,E(I( Z¯))), is a graph with V(I( Z))¯=V(I( Z)) and E(I( Z))¯={xy?E(I( Z)):x,y?V(I( Z))}. In this paper we determine the Laplacian spectrum of the complement of identity graph I( Z2p)¯, for some prime p, that can be constructed by investigating the eigenvalues of I( Z2p)¯. The result shows that all eigenvalues of I( Z2p)¯ are integers. © 2024 Author(s).
Department of Mathematics, Faculty of Mathematics and Science, Universitas Negeri Malang, Jalan Semarang 5, Malang, Indonesia
