H-联图的拟拉普拉斯能量

Quasi-Laplacian Energy Invariant of H-Join Graphs

设图H的顶点集为{1,2,...,k},不交图G1,G2,...,Gk的H-联图(记作G=∨H(G1,G2,...,Gk))是指在Gi(i=1,2,...,k)的基础上,对于H中的任意顶点i、j,若i,j∈E(H),则将Gi的所有点与Gj的每一个点相连所得到的图。特别地,若H=P2,则∨P2(G1∨G2)就是G1与G2的普通联图G1∨G2[4,5]。本文借助H-联图的拉普拉斯谱的性质,刻画了H为完全图以及Gi(i=1,2,...,k)均为n阶图时,∨H(G1,G2,...,Gk)的拟拉普拉斯能量的界。

Let { 1,2,..., k } be the vertex set of graph H, the H-Join graph of a family of disjoint graphs G1 , G2,... , Gk （ denoted by∨ H （ G1, G2 ,..., Gk ） ） is obtained by joining each vertex of Gi to each vertex of Gj whenever i is adjacent toj in H. Particularly, ∨e2 （ G1 ∨ G2 ） is the ordinary join graph G1 ∨G2. In this paper, with the help of property of Laplaeian spectrum of H-Join graphs, we give the bounds for the Quasi-Laplaeian energye invariant of them, when H is a complete graph and Gi is a graph with vertices for any i = 1,2, ... ,k.