Dominion of some graphs
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911346724962304 |
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| author | Allagan, Julian Bobga, Benkam |
| author_facet | Allagan, Julian Bobga, Benkam |
| contents | Given a graph G equals (V,E), a subset S subset of V is a dominating set if every vertex in V minus S is adjacent to some vertex in S. The dominating set with the least cardinality, gamma, is called a gamma-set which is commonly known as a minimum dominating set. The dominion of a graph G, denoted by zeta(G), is the number of its gamma-sets. Some relations between these two seemingly distinct parameters are established. In particular, we present the dominions of paths, some cycles and the join of any two graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24115 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dominion of some graphs Allagan, Julian Bobga, Benkam Combinatorics Discrete Mathematics 05C30 Given a graph G equals (V,E), a subset S subset of V is a dominating set if every vertex in V minus S is adjacent to some vertex in S. The dominating set with the least cardinality, gamma, is called a gamma-set which is commonly known as a minimum dominating set. The dominion of a graph G, denoted by zeta(G), is the number of its gamma-sets. Some relations between these two seemingly distinct parameters are established. In particular, we present the dominions of paths, some cycles and the join of any two graphs. |
| title | Dominion of some graphs |
| topic | Combinatorics Discrete Mathematics 05C30 |
| url | https://arxiv.org/abs/2512.24115 |