Permanental Bounds for the Signless Laplacian Matrix of a Unicyclic Graph with Diameter d

摘要

Let U _n be the set of n-vertex unicyclic graphs, U _n ~d be the set of n-vertex unicyclic graphs of diameter d. In this paper we determine the second-minimum value of signless Laplacian permanent of graphs among U _n; as well we obtain the lower bound for the signless Laplacian permanent of graphs in U _n d. The corresponding extremal graphs are characterized.