Relations between the positive inertia index of a T-gain graph and that of its underlying graph
Received:April 04, 2020  Revised:June 01, 2020
Key Word: Complex unit gain graphs   inertia index  
Fund ProjectL:Natural Science Foundation of Shandong Province
Author NameAffiliationE-mail
Sai Wang XuHai College, China University of Mining and Technology 27624181@qq.com 
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Abstract:
      Let T be the subgroup of the multiplicative group C× consisting of all complex numbers z with |z| = 1. A T-gain graph is a triple Φ = (G, T, φ) ( or short for (G, φ) ) consisting of a simple graph G = (V,E), as the underlying graph of (G, φ), the circle group T and a gain function φ : ?→E → T such that φ(vivj) = φ(vjvi) for any adjacent vertices vi and vj . Let i+(G, φ) (resp, i+(G) ) be the positive inertia index of (G, φ) (resp, G). In this paper, we prove that ?c(G) ≤ i+(G, φ) ? i+(G) ≤ c(G). where c(G) is the cyclomatic number of G, and characterize all the corresponding extremal graphs.
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