不含三圈的k圈图的拟拉普拉斯和拉普拉斯谱半径  

On the signless Laplacian and Laplacian spectral radius of triangle-free k-cyclic graphs

作　　者：何春阳[1,2] 郭曙光[2] 

机构地区：[1]青海师范大学数学系,青海西宁810008 [2]盐城师范学院数学科学学院,江苏盐城224002

出　　处：《高校应用数学学报（A辑）》2014年第3期295-302,共8页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11171290)

摘　　要：k圈图是边数等于顶点数加k-1的简单连通图.文中确定了不含三圈的k圈图的拟拉普拉斯谱半径的上界,并刻画了达到该上界的极图.此外,文中确定了拟拉普拉斯谱半径排在前五位的不含三圈的单圈图,排在前八位的不含三圈的双圈图.最后说明文中所得结论对不含三圈的k圈图的拉普拉斯谱半径也成立.A k-cyclic graph is a connected graph in which the number of edges equals the number of vertices plus k ＋ 1. This paper determines the maximal signless Laplacian spectral radius together with the corresponding extremal graph among all triangle-free k-cyclic graphs of order n. Moreover, this paper gives the first five triangle-free unicyclic graphs on n （n ≥ 8） vertices, and the first eight triangle-free bicyclic graphs on n （n 〉 12） vertices according to the signless Laplacian spectral radius. Finally, the authors of this paper show that the results obtained in this paper also hold for Laplacian spectral radius of triangle-free k-cyclic graphs of order n.

关 键 词：k圈图 不含三圈 拟拉普拉斯谱半径 拉普拉斯谱半径 单圈图 双圈图 

分 类 号：O157[理学—数学]