Complex unit gain bicyclic graphs with rank 2, 3 or 4

2015/11/24 by Yong Lu, Lu, Yong, Ligong Wang +3 · 1 citation
Computer Science · Mathematics · #05C22 #05C50 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.1511.07589

openalex publication_date 2015/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A \mathbbT-gain graph is a triple Φ=(G,\mathbbT,φ) consisting of a graph G=(V,E), the circle group \mathbbT=\z∈ C: |z|=1\ and a gain function φ:\overrightarrowE→ \mathbbT such that φ(e_ij)=φ(e_ji)^-1=φ(e_ji). The rank of \mathbbT-gain graph Φ, denoted by r(Φ), is the rank of the adjacency matrix of Φ. In 2015, Yu, Qu and Tu [ G. H. Yu, H. Qu, J. H. Tu, Inertia of complex unit gain graphs, Appl. Math. Comput. 265(2015) 619--629 ] obtained some properties of inertia of a \mathbbT-gain graph. They characterized the \mathbbT-gain unicyclic graphs with small positive or negative index. Motivated by above, in this paper, we characterize the complex unit gain bicyclic graphs with rank 2, 3 or 4.

Citations

• A survey on the skew energy of oriented graphs

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