【摘要】 设R是一个环.环R的单位图,记为珚G(R),它的顶点为R中的元素,两个顶点x和y相连当且仅当x+y是环R的单位.称图G是整图,如果其邻接矩阵的特征值都是整数.该文证明了对于所有的n,珚G(Zn)都是整图,其中Zn是模n剩余类环.称图G是超能图,若其能量E(G)>2n-2,其中n为图G的顶点数.通过计算珚G(Zn)的能量完全决定了什么时候单位图珚G(Zn)是超能图.更多还原

【Abstract】 Let Rbe aring.The unit graph of R,denoted by珚G(R),is agraph defined on the elements of R,two vertices xand yare adjacent if and only if x+yis aunit of R.A graph Gis integral if all eigenvalues of adjacency matrix of the graph are integers.In this paper,we prove that珚G(Zn)is an integral graph for all n.A graph Gwith nvertices is called ahyperenergy graph if its energy E(G)>2n-2.Finally,through computing the energy of珚G(Zn),we completely determine when珚G(Zn)is ahyperenergy graph.更多还原