English

Unicyclic signed graphs with maximal energy

Combinatorics 2018-09-18 v1

Abstract

Let x1,x2,,xnx_1, x_2, \dots, x_n be the eigenvalues of a signed graph Γ\Gamma of order nn. The energy of Γ\Gamma is defined as E(Γ)=j=1nxj.E(\Gamma)=\sum^{n}_{j=1}|x_j|. Let Pn4\mathcal{P}_n^4 be obtained by connecting a vertex of the negative circle (C4,σ)(C_4,{\overline{\sigma}}) with a terminal vertex of the path Pn4P_{n-4}. In this paper, we show that for n=4,6n=4,6 and n8,n \geq 8, Pn4\mathcal{P}_n^4 has the maximal energy among all connected unicyclic nn-vertex signed graphs, except the cycles C5+,C7+.C_5^+, C_7^+.

Keywords

Cite

@article{arxiv.1809.06206,
  title  = {Unicyclic signed graphs with maximal energy},
  author = {Dijian Wang and Yaoping Hou},
  journal= {arXiv preprint arXiv:1809.06206},
  year   = {2018}
}
R2 v1 2026-06-23T04:08:44.362Z