The index of unbalanced signed complete graphs whose negative-edge-induced subgraph is ${K}_{2,2}$-minor free
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913836709183488 |
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| author | Qin, Mingsong Li, Dan |
| author_facet | Qin, Mingsong Li, Dan |
| contents | Let $Γ=(K_n,H^-)$ 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 $K_{2,2}$-minor free spanning subgraph of $K_n$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_09136 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The index of unbalanced signed complete graphs whose negative-edge-induced subgraph is ${K}_{2,2}$-minor free Qin, Mingsong Li, Dan Combinatorics 05C50, 05C35 Let $Γ=(K_n,H^-)$ 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 $K_{2,2}$-minor free spanning subgraph of $K_n$. |
| title | The index of unbalanced signed complete graphs whose negative-edge-induced subgraph is ${K}_{2,2}$-minor free |
| topic | Combinatorics 05C50, 05C35 |
| url | https://arxiv.org/abs/2505.09136 |