一类混合图的结构及其特征空间

主要讨论具有如下性质的一类连通混合图G:其所有非奇异圈恰有一条公共边,且除了该公共边的端点外,任意两个非奇异圈没有其它交点.本文给出了图G的结构性质,建立了其最小特征值λ1(G)(以及相对应的特征向量)与某个简单图的代数连通度(以及Fiedler向量)之间联系,并应用上述联系证明了λ1(■)≤α(G),其中G是由G通过对其所有无向边定向而获得,α(■)为■的代数连通度.

On Structure and Eigenspace of a Class of Mixed Graphs

This paper mainly discusses a class of mixed graphs with following property:all nonsingular cycles share exactly one common edge and any two nonsingular cycles have no other common vertices except that of the common edge.We gives a structure property of G,then establish a relation between the least eigenvalue λ1(G)of G(and the corresponding eigenvectors)and the algebraic connectivity(and Fiedler vectors)of a certain simple graph,and using the relation show that λ1(G)≤α(■),where is obtained from G by orienting all its unoriented edges and α(■)is the algebraic connectivity of ■.