TY - JOUR
T1 - Complex unit gain bicyclic graphs with rank 2, 3 or 4
AU - Lu, Yong
AU - Wang, Ligong
AU - Xiao, Peng
N1 - Publisher Copyright:
© 2017 Elsevier Inc.
PY - 2017/6/15
Y1 - 2017/6/15
N2 - 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(eij)=φ(eji)−1=φ(eji)‾. 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.
AB - 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(eij)=φ(eji)−1=φ(eji)‾. 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.
KW - Bicyclic graph
KW - Complex unit gain graph
KW - Rank
KW - T-gain graph
UR - http://www.scopus.com/inward/record.url?scp=85014218332&partnerID=8YFLogxK
U2 - 10.1016/j.laa.2017.02.031
DO - 10.1016/j.laa.2017.02.031
M3 - 文章
AN - SCOPUS:85014218332
SN - 0024-3795
VL - 523
SP - 169
EP - 186
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
ER -