给定阶及边独立数和圈数的图的谱半径

摘要

令U(n,i,r)表示阶是n、边独立数是i和圈数是r的简单连通图的集合,这里图的任意两个圈至多有一个公共项点.当i≥r+1时,对任意的G∈U(n,i,r),得到了G的谱半径的精确上界和达到上界的所有极图.这一结果推广了树、单圈图和双圈图谱半径的许多已有结论.%Let U(n, i, r) be the set of simple and connected graphs with order n, edge independence number i and cycle number r in which arbitrary two cycles have at most a common vertex.We obtain the upper bound for spectral radius of graphs in U(n, i, r) (i ≥ r + 1) and give all such graphs that their spectral radius reach the upper bounds. These results generalize many ones on the spectral radius of trees, unicyclic graphs and bicyclic graphs.