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Recenzirano
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Chen, Fan; Yuan, Xiying
Applied mathematics and computation, 09/2024, Letnik: 477Journal Article
Let G˙ be an unbalanced signed graph. In this paper, we establish that e(G˙)⩽12(n2−n)−(n−3) and ρ(G˙)⩽n−2 if G˙ does not contain unbalanced K4 as a signed subgraph. Moreover, comprehensive characterizations of the extremal signed graphs have been obtained. •The situation that the index of signed graph equals to the spectral radius of underlying graph has been characterized.•We determine the Turán number of K4− in unbalanced signed graph, and we characterize all the extremal signed graphs.•We solve the spectral Turán problem among all K4−-free unbalanced signed graphs.
