恰含两个圈的二部图的能量

Energy of bipartite graphs with exactly two cycles

设λ1,λ2,…,λn是n阶图G的特征值,图G的能量是E(G)=|λ1|+|λ2|+…+|λn|.设G(n)是n个顶点n+1条边的恰有两个圈的连通二部图的集合,Z(n;4,4)是G(n)中的一个图,它的两个长为4的圈恰有一个公共点,其余n-7个点都是悬挂点且均与这个公共点相邻.文中证明了Z(n;4,4)是G(n)中具有最小能量的图.

The energy of a graph G with n vertices is defined as E(G)=｜λ_1｜+｜λ_2｜+...+｜λ_n｜,where λ_1,λ_2,...,λ_n are the eignvalues of G.Let G(n) be the set of connected bipartite graphs with n vertices,n+1 edges and exactly two cycles, and let Z(n;4,4) be the graph in G(n) whose two cycles have lengths four and share a common vertex,to which the rest n-7 pendant vertices are adjacent. The paper proves that Z(n;4,4) is the unique graph with minimal energy in G(n).