按Laplace谱半径对圈长和阶数固定的单圈图的排序

Unicyclic graphs ordering with fixed number vertices and cycle length by their Laplace spectral radii

研究了圈长和阶数固定的单圈图按其Laplace谱半径排序的问题.通过对单圈图的结构分析,得到了一些移接变换对单圈图的最大Laplace特征值的影响;然后利用这些结论,得出了顶点数为n,圈长为l的单圈图C(n,l)(n≥l+3,l≥5)按其最大Laplace特征值从大到小的顺序依次排在前三位的单圈图.

Ordering unicyclic graphs with fixed number vertices and cycle length by their largest Laplacian eigenvalues are studied. Through the analyses of unicyclic graphs, some transformations which change the largest Laplacian eigenvalues of unicyclic graphs are given. By applying these results, the top three in the order of unicyclic graphs C（n,ι）（n≥ι＋3,ι≥5） by their largest Laplacian eigenvalues are given.