【摘 要】
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Let T be the subgroup of the multiplicative group Cx consisting of all complex numbers z with |z| = 1.A T-gain graph is a triple Φ =(G,T,ψ)(or short for(G,ψ)
【机 构】
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School of Mathematics,China University of Mining and Technology,Jiangsu 221116,P.R.China;Xuhai Colle
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Let T be the subgroup of the multiplicative group Cx consisting of all complex numbers z with |z| = 1.A T-gain graph is a triple Φ =(G,T,ψ)(or short for(G,ψ))consisting of a simple graph G =(V,E),as the underlying graph of(G,ψ),the circle group T and a gain function ψ:→E → T such that ψ(vivj)=- ψ(vjvi)for any adjacent vertices vi and vj.Let i+(G,ψ)(resp.,i+(G))be the positive inertia index of(G,ψ)(resp.,G).In this paper,we prove that-c(G)≤i+(G,ψ)-i+(G)≤c(G),where c(G)is the cyclomatic number of G,and characterize all the corresponding extremal graphs.
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