Extremed signed graphs for triangle
Dijian Wang, Yaoping Hou, Deqiong Li

TL;DR
This paper investigates the extremal properties of signed graphs related to the Turán problem, focusing on bounds for edges, negative edges, and spectral radius in $C_3^-$-free graphs, and characterizes the extremal structures.
Contribution
It provides new bounds and characterizations for the maximum edges, negative edges, and spectral radius in $C_3^-$-free signed graphs, introducing specific extremal graph constructions.
Findings
Maximum edges in $C_3^-$-free signed graphs characterized.
Maximum negative edges achieved by specific extremal graphs.
Spectral radius bounds established with equality conditions.
Abstract
In this paper, we study the Tur\'{a}n problem of signed graphs version. Suppose that is a connected unbalanced signed graph of order with edges and negative edges, and let be the spectral radius of The signed graph () is obtained from an all-positive clique with () and two isolated vertices and by adding negative edge and positive edges Firstly, we prove that if is -free, then with equality holding if and only if Moreover, with equality holding if and only if $\dot{G}^{s,t}=…
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Taxonomy
TopicsMagnetism in coordination complexes · Organometallic Complex Synthesis and Catalysis · Graph theory and applications
