Unicyclic signed graphs with maximal energy

2018/09/17 by Dijian Wang, Yaoping Hou, Wang, Dijian +1
Mathematics · Computer Science · #Graph theory and applications #Advanced Graph Theory Research #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.1809.06206

Abstract

Let x₁, x₂, …, x_n be the eigenvalues of a signed graph Γ of order n. The energy of Γ is defined as E(Γ)=∑ⁿ_j=1|x_j|. Let P_n⁴ be obtained by connecting a vertex of the negative circle (C₄,σ) with a terminal vertex of the path P_n-4. In this paper, we show that for n=4,6 and n ≥ 8, P_n⁴ has the maximal energy among all connected unicyclic n-vertex signed graphs, except the cycles C₅⁺, C₇⁺.

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