关于图的代数连通度的注记(英文)

Note on the Algebraic Connectivity of a Graph

n阶连通图G的代数连通度、点连通度和边连通度分别记作α(G) ,κ(G)和λ(G) .本文给出了当 2 κ(G) n- 2时 ,α(G) =κ(G)成立的充要条件 ,讨论了α(G)的代数重数以及相应于特征值α(G)的特征向量的性质 .最后给出了当 1 λ(G) n- 2时 ,α(G) =λ(G)的充要条件 .

Let G be a connected graph of order n whose algebraic connectivity, vertex connectivity, and edge connectivity are α(G), κ(G), and λ(G), respectively. First, an equivalent condition is given for α(G)=κ(G) when 2κ(G)n-2 . And the algebraic multiplicity of α(G) and the property of eigenvectors corresponding to α(G) are discussed when the above equality holds. By the obtained results, the equivalent condition for α(G)=λ(G) is also established when 1λ(G)n-2 .