Relation between the rank of a signed graph and the rank of its underlying graph
Relation between the rank of a signed graph and the rank of its underlying graph
复制标题
DOI：
10.1080/03081087.2018.1497007
复制
发表时间：
2018-07
影响因子：
1.1
通讯作者：
Shujing Wang
中科院分区：
文献类型：
--
作者：
Shujing Wang
有符号图是每条边都有符号的图，其中G是的底层图。设为的邻接矩阵，为G的邻接矩阵。，写为（代表），指的是（职位）的等级。）. 一个自然而有趣的问题是：一个有符号图的秩和它的底层图的秩之间的关系是什么？本文将重点研究这一问题。上的下界和上界是确定的。对所有相应的极值符号图分别进行了表征。
ABSTRACT A signed graph is a graph with a sign attached to each of its edges, where G is the underlying graph of . Let denote the adjacency matrix of , and be the adjacency matrix of G. The rank of G (resp. ), written as (resp. ), refers to the rank of (resp. )). A natural and interesting problem is: What is the relation between the rank of a signed graph and the rank of its underlying graph? In this paper, we focus our attention on this problem. Sharp lower bounds and upper bounds on are determined. All the corresponding extremal signed graphs are characterized, respectively.