单圈偶图是边数等于顶点数的简单连通偶图,△(G)表示图G的最大度.文中给出了最大度为△(≥2/n+1)的n阶单圈偶图的谱半径的上界,并刻画了达到该上界的图,文中还证明了当△(G)≥「3/2n+1」+1时,n(≥8)阶单圈偶图G的谱半径随着最大度的递增而严格递增,并在此基础上给出了谱半径排在前17位的n(≥16)阶单圈偶图.
A unicyclic bipartite graph is a connected bipartite graph in which the number of edges equals the number of vertices. Denote by △(G) the maximum degree of graph G. In this paper we determine the upper bound of spectral radii of unicyclic bipartite graphs on n vertices with fixed maximum degree A △(≥2/n+1) and characterize the graph in which the maximal spectral radius is attained. We also prove that the spectral radius of a unicyclic bipartite graph G on n (≥ 8) vertices strictly increases with its maximum degree when △(G)≥「3/2n+1」+1. On this basis we give the first seventeen unicyclic bipartite graphs on n n(≥16) vertices according to the spectral radius.