单位凯莱图及其补图的(无符号)拉普拉斯能量

THE(SIGNLESS)LAPLACIAN ENERGY OF UNITARY CAYLEY GRAPHS AND ITS COMPLEMENTARY GRAPHS

令Z_(n)为模n的剩余类加群,单位凯莱图X_(n)是指以V(X_(n))=Z_(n)为顶点集,E(X_(n))={(a,b):a,b∈Z_(n),a-b∈U_(n)}为边集的简单无向图,其中U_(n)={a∈Z_(n):gcd(a,n)=1}。利用欧拉函数给出了单位凯莱图X_(n)及其补图X_(n)的拉普拉斯能量和无符号拉普拉斯能量。

Let Z_(n) be the residual class additive group of modul n,and the unitary Cayley graph X_(n) is a simple undirected graph with V(X_(n))=Z_(n) as its vertex set and E(X_(n))={(a,b):a,b∈Z_(n),a-b∈U_(n)}as the edge set,where U_(n)={a∈Z_(n):gcd(a,n)=1}.The Laplacian energy,signless Laplacian energy of unitary Cayley graphs and its complementary graphs are given by using Euler function.