An edge-grafting theorem on Laplacian spectra of graphs and its application

作者：Zhai, Mingqing; Liu, Ruifang; Shu, Jinlong^*

来源：Linear and Multilinear Algebra, 2011, 59(3): 303-315.

DOI：10.1080/03081080903441499

• edge-grafting
• Laplacian spectral radius
• diameter
• unicyclic graph

Let U(n, d) be the class of unicyclic graphs on n vertices with diameter d. This article presents an edge-grafting theorem on Laplacian spectra of graphs. By applying this theorem, we determine the unique graph with the maximum Laplacian spectral radius in U(n, d). This extremal graph is different from that for the corresponding problem on the adjacency spectral radius as done by Liu et al. [Q. Liu, M. Lu, and F. Tian, On the spectral radius of unicyclic graphs with fixed diameter, Linear Algebra Appl. 420 (2007), 449-457].

• 出版日期2011
• 单位滁州学院; 华东师范大学