斜秩等于围长的定向图的刻画  

Characterization of oriented graphs with skew-rank equaling to girth

作　　者：王震 WANG Zhen(School of Mathematics and Big Data,Anhui University of Science and Technology,Huainan 232001,China)

机构地区：[1]安徽理工大学数学与大数据学院,安徽淮南232001

出　　处：《哈尔滨商业大学学报（自然科学版）》2023年第2期212-220,共9页Journal of Harbin University of Commerce：Natural Sciences Edition

摘　　要：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.

关 键 词：斜秩 定向图 围长 定向路 孪生点 

分 类 号：O157.5[理学—数学]