Inertia of complex unit gain graphs

Guihai Yu, Hui Qu and Jianhua Tu

Applied Mathematics and Computation, 2015, vol. 265, issue C, 619-629

Abstract: Let T={z∈C:|z|=1} be a subgroup of the multiplicative group of all nonzero complex numbers C×. A T-gain graph is a triple Φ=(G,T,φ) consisting of a graph G=(V,E), the circle group T and a gain function φ:E→→T such that φ(eij)=φ(eji)−1=φ(eji)¯. The adjacency matrix A(Φ) of the T-gain graph Φ=(G,φ) of order n is an n × n complex matrix (aij), where aij={φ(eij),ifviisadjacenttovj,0,otherwise.Evidently this matrix is Hermitian. The inertia of Φ is defined to be the triple In(Φ)=(i+(Φ),i−(Φ),i0(Φ)), where i+(Φ),i−(Φ),i0(Φ) are numbers of the positive, negative and zero eigenvalues of A(Φ) including multiplicities, respectively. In this paper we investigate some properties of inertia of T-gain graph.

Keywords: Inertia; Complex unit gain graph; Tree; Unicyclic graph (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:265:y:2015:i:c:p:619-629

DOI: 10.1016/j.amc.2015.05.105

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