On cubic rainbow domination regular graphs
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912072545075200 |
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| author | Kuzman, Bostjan |
| author_facet | Kuzman, Bostjan |
| contents | A $d$-regular graph $X$ is called $d$-rainbow domination regular or $d$-RDR, if its $d$-rainbow domination number $γ_{rd}(X)$ attains the lower bound $n/2$ for $d$-regular graphs, where $n$ is the number of vertices. In the paper, two combinatorial constructions to construct new $d$-RDR graphs from existing ones are described and two general criteria for a vertex-transitive $d$-regular graph to be $d$-RDR are proven. A list of vertex-transitive 3-RDR graphs of small orders is produced and their partial classification into families of generalized Petersen graphs, honeycomb-toroidal graphs and a specific family of Cayley graphs is given by investigating the girth and local cycle structure of these graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_10662 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On cubic rainbow domination regular graphs Kuzman, Bostjan Combinatorics A $d$-regular graph $X$ is called $d$-rainbow domination regular or $d$-RDR, if its $d$-rainbow domination number $γ_{rd}(X)$ attains the lower bound $n/2$ for $d$-regular graphs, where $n$ is the number of vertices. In the paper, two combinatorial constructions to construct new $d$-RDR graphs from existing ones are described and two general criteria for a vertex-transitive $d$-regular graph to be $d$-RDR are proven. A list of vertex-transitive 3-RDR graphs of small orders is produced and their partial classification into families of generalized Petersen graphs, honeycomb-toroidal graphs and a specific family of Cayley graphs is given by investigating the girth and local cycle structure of these graphs. |
| title | On cubic rainbow domination regular graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2410.10662 |