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arXiv · 1809.06206

Unicyclic signed graphs with maximal energy

Dijian Wang·Yaoping Hou
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Abstract

Let $x_1, x_2, \dots, x_n$ be the eigenvalues of a signed graph $Γ$ of order $n$. The energy of $Γ$ is defined as $E(Γ)=\sum^{n}_{j=1}|x_j|.$ Let $\mathcal{P}_n^4$ be obtained by connecting a vertex of the negative circle $(C_4,{\overlineσ})$ with a terminal vertex of the path $P_{n-4}$. In this paper, we show that for $n=4,6$ and $n \geq 8,$ $\mathcal{P}_n^4$ has the maximal energy among all connected unicyclic $n$-vertex signed graphs, except the cycles $C_5^+, C_7^+.$

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Dijian Wang, Yaoping Hou. 2018-09-17. Unicyclic signed graphs with maximal energy. https://arxiv.org/abs/1809.06206

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