Total coalition graphs of cycles and paths Full article
| Journal |
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304 |
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| Output data | Year: 2025, Volume: 22, Number: 1, Pages: 662-669 Pages count : 8 DOI: 10.33048/semi.2025.22.043 | ||||
| Tags | total coalition graph, total dominating set | ||||
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0017 |
Abstract:
A subset of vertices in a graph G is a total dominating set if every vertex of G is adjacent to at least one vertex within the subset. Two non-total dominating sets form a total coalition in a graph if their union is a total dominating set. A partition π of graph vertices into non-total dominating sets is a total coalition partition if every set of π forms a total coalition set with at least one other set of π. Vertices of the total coalition graph TCG(G,π) correspond with the sets of π, and two vertices are adjacent in TCG(G,π) if and only if the corresponding sets constitute a total coalition. We show that C4k is a universal total coalition cycle for k ≥2, that is, a cycle whose total coalition partitions generate all possible total coalition graphs of cycles. We also demonstrate that Pn is a universal total coalition path for n ≥ 5.
Cite:
Dobrynin A.A.
, Golmohammadi H.
Total coalition graphs of cycles and paths
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2025. V.22. N1. P.662-669. DOI: 10.33048/semi.2025.22.043
Total coalition graphs of cycles and paths
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2025. V.22. N1. P.662-669. DOI: 10.33048/semi.2025.22.043
Dates:
| Submitted: | Sep 30, 2024 |
| Published print: | Jul 4, 2025 |
| Published online: | Jul 4, 2025 |
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