On Laplacian Coefficients of Bipartite Bicyclic Graphs

Abstract

The Laplacian coefficients of bipartite bicyclic graphs were investigated.All the bipartite bicyclic graphs were classified into three categories.The graph with the smallest k-th coefficient of each category was obtained by using α-transform and Laplacian characteristic polynominal of the graph,and then the graph with the smallest k-th coefficient among all bipartite bicyclic graphs of order n was obtained by using Laplacian characteristic polynominal of the graph.