Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8898026 | Linear Algebra and its Applications | 2018 | 11 Pages |
Abstract
The spectral radius Ï(G) of a graph G is the largest eigenvalue of the adjacency matrix A(G). Suppose a graph G0 maximizes the spectral radius over the class of graphs of order n with fixed minimum degree δ and edge connectivity κâ²<δ. In this paper, we mainly show that G0â
Bn,δκâ², where Bn,δκⲠis obtained by adding κⲠedges between Kδ+1 and Knâδâ1. A property of the adjacency matrix of G0 is also obtained. Moreover, graphs that maximize Ï(G) over the class of graphs with minimum degree δ and edge-connectivity κâ², for κâ²=0,1,2,3,δ, are completely determined.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Wenjie Ning, Mei Lu, Kun Wang,