【摘要】 设G为n阶连通混合图.当G为非奇异,其最小非零特征值为λ1(G)>0.给G的每条无向边指定任意一个方向,得到与G有相同基础图的全定向图G,则G的最小非零特征值为其代数连通度(或次小特征值)λ2(G)=α(G)>0.本文主要讨论λ1(G)与α(G)的关系,证明了:当G恰含一个非奇异圈,有λ1(G)≤α(G).更多还原

【Abstract】 Let G be a mixed graph of order n.If G is nonsingular, its least nonzero eigenvalue λ₁（G）>0.Assigning an arbitrary direction to each undirected edge of G, we obtain an all-oriented graph G with the same underlying graph as that of G.Then the least nonzero eigenvalue of G is the algebraic connectivity （or the second least eigenvalue） λ₂（G）=α（G）>0.This paper mainly discuss the relation between λ₁（G） and α（G）, and show that if G contains exactly one nonsingular cycle, then λ₁（G）≤α（G）.更多还原