Maximizing signless Laplacian or adjacency spectral radius of graphs subject to fixed connectivity

• Published in: Linear algebra and its applications Vol. 433; no. 6; pp. 1180 - 1186
• Main Authors: Ye, Miao-Lin, Fan, Yi-Zheng, Wang, Hai-Feng
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01.11.2010; Elsevier
• Subjects: Adjacency matrix; Algebra; Applied sciences; Combinatorics; Combinatorics. Ordered structures; Connectivity; Exact sciences and technology; Flows in networks. Combinatorial problems; Graph; Graph theory; Linear and multilinear algebra, matrix theory; Mathematics; Operational research and scientific management; Operational research. Management science; Sciences and techniques of general use; Signless Laplacian matrix; Spectral radius; Graph; Signless Laplacian matrix; 05C50; Spectral radius; 05C40; Adjacency matrix; Connectivity; 90C27; Perron value; Graph theory; Combinatorial optimization; Laplacian; Upper bound
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2010.04.045

In this paper, we characterize the graphs with maximum signless Laplacian or adjacency spectral radius among all graphs with fixed order and given vertex or edge connectivity. We also discuss the minimum signless Laplacian or adjacency spectral radius of graphs subject to fixed connectivity. Consequently we give an upper bound of signless Laplacian or adjacency spectral radius of graphs in terms of connectivity. In addition we confirm a conjecture of Aouchiche and Hansen involving adjacency spectral radius and connectivity.