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Inertia of complex unit gain graphs

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  • Yu, Guihai
  • Qu, Hui
  • Tu, Jianhua

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.

Suggested Citation

  • Yu, Guihai & Qu, Hui & Tu, Jianhua, 2015. "Inertia of complex unit gain graphs," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 619-629.
  • Handle: RePEc:eee:apmaco:v:265:y:2015:i:c:p:619-629
    DOI: 10.1016/j.amc.2015.05.105
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    Cited by:

    1. Köberle, Alexandre C. & Garaffa, Rafael & Cunha, Bruno S.L. & Rochedo, Pedro & Lucena, André F.P. & Szklo, Alexandre & Schaeffer, Roberto, 2018. "Are conventional energy megaprojects competitive? Suboptimal decisions related to cost overruns in Brazil," Energy Policy, Elsevier, vol. 122(C), pages 689-700.
    2. Lang, Rongling & Li, Tao & Mo, Desen & Shi, Yongtang, 2016. "A novel method for analyzing inverse problem of topological indices of graphs using competitive agglomeration," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 115-121.
    3. Yong Lu & Ligong Wang & Qiannan Zhou, 2019. "The rank of a complex unit gain graph in terms of the rank of its underlying graph," Journal of Combinatorial Optimization, Springer, vol. 38(2), pages 570-588, August.
    4. Guihai Yu & Hui Qu, 2018. "More on Spectral Analysis of Signed Networks," Complexity, Hindawi, vol. 2018, pages 1-6, October.

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