Chromatic Index of Signed Generalized Book Graphs and Signed Complete Graphs
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914339929194496 |
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| author | Sehrawat, Deepak Rohit |
| author_facet | Sehrawat, Deepak Rohit |
| contents | A signed graph $(G,σ)$ consists of a graph $G$ and the signature $σ: E(G) \rightarrow \{+1,-1\}$. An incidence of $G$ is a pair $(v,e)$, where $v$ is one of the end vertices of an edge $e \in E(G)$. A proper $q$-edge coloring $γ$ of signed graph $(G,σ)$ is an assignment of colors to incidences satisfying that $γ(v,e) = - σ(e) γ(w,e)$ for every edge $e=vw$ and for any two incidences $(v,e)$ and $(v,f)$, involving the same vertex, $γ(v,e) \neq γ(v,f)$. The chromatic index of a signed graph $(G,σ)$, denoted by $χ'(G,σ)$, is the minimum number $q$ for which $(G,σ)$ has a proper $q$-edge coloring. In this paper, we determine the chromatic index of signed generalized book graphs. We also determine the chromatic index of signed complete graphs of order up to six. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_18244 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Chromatic Index of Signed Generalized Book Graphs and Signed Complete Graphs Sehrawat, Deepak Rohit Combinatorics 05C15, 05C22 A signed graph $(G,σ)$ consists of a graph $G$ and the signature $σ: E(G) \rightarrow \{+1,-1\}$. An incidence of $G$ is a pair $(v,e)$, where $v$ is one of the end vertices of an edge $e \in E(G)$. A proper $q$-edge coloring $γ$ of signed graph $(G,σ)$ is an assignment of colors to incidences satisfying that $γ(v,e) = - σ(e) γ(w,e)$ for every edge $e=vw$ and for any two incidences $(v,e)$ and $(v,f)$, involving the same vertex, $γ(v,e) \neq γ(v,f)$. The chromatic index of a signed graph $(G,σ)$, denoted by $χ'(G,σ)$, is the minimum number $q$ for which $(G,σ)$ has a proper $q$-edge coloring. In this paper, we determine the chromatic index of signed generalized book graphs. We also determine the chromatic index of signed complete graphs of order up to six. |
| title | Chromatic Index of Signed Generalized Book Graphs and Signed Complete Graphs |
| topic | Combinatorics 05C15, 05C22 |
| url | https://arxiv.org/abs/2602.18244 |