Upper bounds on the spectral radius of book-free and/or K-2,K-l-free graphs

作者：Shi Lingsheng^*; Song Zhipeng

来源：Linear Algebra and Its Applications, 2007, 420(2-3): 526-529.

DOI：10.1016/j.laa.2006.08.007

• spectral radius
• girth
• book-free graph
• strongly regular graph

The spectral radius p(G) of a graph G is the largest eigenvalue of its adjacency matrix. Let B-k denote a book with k pages. In this paper, we generalize a result of Lu et al. [M. Lu, H. Liu, F. Tian, A new upper bound for the spectral radius of graphs with girth at least 5, Linear Algebra Appl. 414 (2006) 512-516] on the upper bound for the spectral radius of connected graphs with girth at least 5 to connected {Bk+1, K2.l+1}-free graphs G of order n with maximum degree Delta as follows:
p (G) <= [k-l+ root(k-l)(2)+4 Delta+4l(n-1)]/2
with equality if and only if G is a strongly regular graph with parameters (Delta, k, l). This implies sharp upper bounds for book-free or K2.l-free graphs.

• 出版日期2007-1-15
• 单位清华大学