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In this paper, we study the Tur\'{a}n problem of signed graphs version. Suppose that $\dot{G}$ is a connected unbalanced signed graph of order $n$ with $e(\dot{G})$ edges and $e^-(\dot{G})$ negative edges, and let $\rho(\dot{G})$ be the spectral radi
Externí odkaz:
http://arxiv.org/abs/2212.11460
A mixed multigraph is obtained from an undirected multigraph by orienting a subset of its edges. In this paper, we study a new Hermitian matrix representation of mixed multigraphs, give an introduction to cospectral operations on mixed multigraphs, a
Externí odkaz:
http://arxiv.org/abs/2206.12777
The Hoffman program with respect to any real or complex square matrix $M$ associated to a graph $G$ stems from Hoffman's pioneering work on the limit points for the spectral radius of adjacency matrices of graphs does not exceed $\sqrt{2+\sqrt{5}}$.
Externí odkaz:
http://arxiv.org/abs/2203.01530
Publikováno v:
In Linear Algebra and Its Applications 15 January 2024 681:47-65
Akademický článek
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Publikováno v:
In Discrete Mathematics June 2023 346(6)
Autor:
Wang, Dijian, Hou, Yaoping
Let $x_1, x_2, \dots, x_n$ be the eigenvalues of a signed graph $\Gamma$ of order $n$. The energy of $\Gamma$ is defined as $E(\Gamma)=\sum^{n}_{j=1}|x_j|.$ Let $\mathcal{P}_n^4$ be obtained by connecting a vertex of the negative circle $(C_4,{\overl
Externí odkaz:
http://arxiv.org/abs/1809.06206
Publikováno v:
Linear & Multilinear Algebra; Nov2024, Vol. 72 Issue 16, p2719-2731, 13p
Publikováno v:
In Discrete Mathematics December 2021 344(12)