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- Title
Coalition of cubic graphs of order at most 10.
- Authors
Alikhani, Saeid; Golmohammadi, Hamidreza; Konstantinova, Elena V.
- Abstract
The coalition in a graph G consists of two disjoint sets of vertices V1 and V2, neither of which is a dominating set but whose union V1 ∪ V2, is a dominating set. A coalition partition in a graph G is a vertex partition π = {V1, V2, . . ., Vk} such that every set Vi ∈ π is not a dominating set but forms a coalition with another set Vj ∈ π which is not a dominating set. The coalition number C(G) equals the maximum k of a coalition partition of G. In this paper, we compute the coalition numbers of all cubic graphs of order at most 10.
- Subjects
GRAPHIC methods; GEOMETRY; MATHEMATICS; GEOMETRIC vertices; PETERSEN graphs
- Publication
Communications in Combinatorics & Optimization, 2024, Vol 9, Issue 3, p437
- ISSN
2538-2128
- Publication type
Article
- DOI
10.22049/cco.2023.28328.1507