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**Coalition of cubic graphs of order at most 10.** / Alikhani, Saeid; Голмохаммади, Хамидреза ; Константинова, Елена Валентиновна.

Research output: Contribution to journal › Article › peer-review

Alikhani, S, Голмохаммади, Х & Константинова, ЕВ 2024, 'Coalition of cubic graphs of order at most 10', *Communications in Combinatorics and Optimization*, vol. 9, no. 3, pp. 437-450. https://doi.org/10.22049/CCO.2023.28328.1507

Alikhani, S., Голмохаммади, Х., & Константинова, Е. В. (2024). Coalition of cubic graphs of order at most 10. *Communications in Combinatorics and Optimization*, *9*(3), 437-450. https://doi.org/10.22049/CCO.2023.28328.1507

Alikhani S, Голмохаммади Х, Константинова ЕВ. Coalition of cubic graphs of order at most 10. Communications in Combinatorics and Optimization. 2024 Sept;9(3):437-450. Epub 2023 Apr 10. doi: 10.22049/CCO.2023.28328.1507

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title = "Coalition of cubic graphs of order at most 10",

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 κ of a coalition partition of G. In this paper, we compute the coalition numbers of all cubic graphs of order at most 10.",

keywords = "coalition, cubic graphs, Petersen graph",

author = "Saeid Alikhani and Хамидреза Голмохаммади and Константинова, {Елена Валентиновна}",

note = "The research by Hamidreza Golmohammadi and Elena V. Konstantinova was supported by the Russian Science Foundation under grant no. 23-21-00459.",

year = "2024",

month = sep,

doi = "10.22049/CCO.2023.28328.1507",

language = "English",

volume = "9",

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journal = "Communications in Combinatorics and Optimization",

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AU - Alikhani, Saeid

AU - Голмохаммади, Хамидреза

AU - Константинова, Елена Валентиновна

N1 - The research by Hamidreza Golmohammadi and Elena V. Konstantinova was supported by the Russian Science Foundation under grant no. 23-21-00459.

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Y1 - 2024/9

N2 - 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 κ of a coalition partition of G. In this paper, we compute the coalition numbers of all cubic graphs of order at most 10.

AB - 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 κ of a coalition partition of G. In this paper, we compute the coalition numbers of all cubic graphs of order at most 10.

KW - coalition

KW - cubic graphs

KW - Petersen graph

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JO - Communications in Combinatorics and Optimization

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