斜秩等于围长的定向图的刻画

Characterization of oriented graphs with skew-rank equaling to girth

设G^(σ)是定向图,S(G^(σ))是其斜邻接矩阵.图G^(σ)的斜秩sr(G^(σ))定义为其斜邻接矩阵的秩.图G^(σ)的围长,记为g(G),定义为其基础图G中最短圈的长度.刻画了斜秩等于围长的定向双圈图,定向三圈图进而推广至所有定向含圈图.

Let G^(σ)be an oriented bicycle graph order of n,and S(G^(σ))be its skew-adjacency matrix.The skew-rank of graph G^(σ),denoted by sr(G^(σ)),was defined to be the rank of its skew-adjacency matrix,and the girth of graph G^(σ),denoted as g(G),was defined to be the length of its shortest cycle of its underlying graph G.In this paper,the oriented bicycle graphs and oriented tricycle graphs with sr(G^(σ))=g(G)were characterized and extended to all oriented cyclic graphs.