关键词: 整循环图, 能量, 特征值, 超能图, Cartesian积

Abstract: Circulant graphs are an important class of interconnection networks in parallel and distributed computing. The energy [E(G)] of a graph [G] is the sum of the absolute values of the eigenvalues of [G.] A graph [G] with [n] vertices is said to be “hyperenergetic” if [E(G)>2n-2.] A graph is called circulant if it is Cayley graph on the circulant group, i.e.its adjacency matrix is circulant. A graph is called integral if all eigenvalues of its adjacency matrix are integers. According to Ramanujans sum, using Euler function and the Mobius function, this paper studies the properties of hyperenergetic of integral circulant graphs. Using the Cartesian product of two graphs, it also constructs hyperenergetic integral circulant graphs.

Key words: integral circulant graphs, energy, eigenvalues, hyperenergetic graphs, Cartesian product