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This analysis shows the maximum index of signed complete graphs in the context of K_{2,2}-minor free structures, indicating their extremal characteristics.
Let Γ=(Kₙ,H⁻) be a signed complete graph with the negative edges induced subgraph H. According to the properties of the negative-edge-induced subgraph, characterizing the extremum problem of the index of the signed complete graph is a concern in signed graphs. A graph G is called H-minor free if G has no minor which is isomorphic to H. In this paper, we characterize the extremal signed complete graphs that achieve the maximum and the second maximum index when H is a K2,2-minor free spanning subgraph of Kₙ.
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Qin et al. (2025) studied this question.
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