On connected signed graphs with rank equal to girth
On connected signed graphs with rank equal to girth
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在秩等于周长的连通有符号图上
DOI：
10.1016/j.laa.2022.06.019
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发表时间：
2022-06
影响因子：
1.1
通讯作者：
Bit-Shun Tam
中科院分区：
文献类型：
--
作者：
Qi Wu;Yong Lu;Bit-Shun Tam
设Γ =（G，σ）是一个带符号图.Γ的秩是Γ的邻接矩阵的秩。若Γ的基础图G至少有一个圈，则Γ的围长（记为gr（Γ））是G中最短圈的长度。Zhou et al（2021）已经确定了秩等于gr（G）（或gr（G）− 2）的连通图G。在本文中，我们将他们的工作扩展到设置的符号图。
Let Γ = ( G , σ ) be a signed graph. The rank of Γ is the rank of the adjacency matrix of Γ. If the underlying graph G of Γ has at least one cycle, then the girth of Γ, denoted by gr ( Γ ) , is the length of the shortest cycle in G . Zhou et al (2021) have identified connected graphs G with rank equal to gr ( G ) (or gr ( G ) − 2 ). In this paper, we extend their work to the setting of signed graphs.