给定独立数的双圈图的最大拟拉普拉斯谱半径(英文)

Maximal signless Laplacian spectral radius of bicyclic graphs with given independence number

设B(n,α)是独立数为α的n阶双圈图,B_1(n,α)是由B(n,α)中含有两个边不交的圈构成的双圈图子集,B_2(n,α)=B(n,α)\B_1(n,α).文中分别研究了B_1(n,α)和B_2(n,α)中具有最大拟拉普拉斯谱半径的极图.进一步地,得到了B(n,α)中拟拉普拉斯谱半径的上界,并给出达到上界的极图.

Let B（n,α）be the class of bicyclic graphs on n vertices with independence numberα.Let B_1（n,α）be the subclass of B（n,α）consisting of all bicyclic graphs with two edge-disjoint cycles and B_2（n,α）=B（n,α）／B_1（n,α）.This paper determined the unique graph with the maximal signless Laplacian spectral radius among all graphs in B_1（n,α） and B_2（n,α）,respectively.Furthermore,the upper bound of the signless Laplacian spectral radius and the extremal graph for B（n,α）were also obtained.