Complex unit gain bicyclic graphs with rank 2, 3 or 4
Complex unit gain bicyclic graphs with rank 2, 3 or 4
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DOI：
10.1016/j.laa.2017.02.031
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发表时间：
2015-11
期刊：
影响因子：
--
通讯作者：
Yong Lu;Ligong Wang;Peng Xiao
中科院分区：
文献类型：
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作者：
Yong Lu;Ligong Wang;Peng Xiao
T-增益图是由图G=（V，E）、圈群T={z∈ C：|z| = 1}和增益函数φ：E→ T，使得φ（e i j）= φ（e j i）− 1= φ（e j i）。T-增益图Φ的秩，记为r（Φ），是Φ的邻接矩阵的秩。Yu等人（2015）[8]得到了T-gain图的惯性的一些性质。他们刻画了具有小正指数或小负指数的T-增益单圈图。受此启发，本文刻画了秩为2，3，4的复单位增益连通双圈图。
A T-gain graph is a triple Φ=(G, T, φ) consisting of a graph G=(V, E), the circle group T={z∈ C:| z|= 1} and a gain function φ: E→→ T such that φ (e i j)= φ (e j i)− 1= φ (e j i)‾. The rank of T-gain graph Φ, denoted by r (Φ), is the rank of the adjacency matrix of Φ. Yu et al.(2015)[8] obtained some properties of inertia of a T-gain graph. They characterized the T-gain unicyclic graphs with small positive or negative index. Motivated by above, in this paper, we characterize the complex unit gain connected bicyclic graphs with rank 2, 3 or 4.