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On cubic graphs having the maximum coalition number. / Dobrynin, A. A.; Golmohammadi, H.

In: Siberian Electronic Mathematical Reports, Vol. 21, No. 1, 2024, p. 363-369.

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

Harvard

Dobrynin, AA & Golmohammadi, H 2024, 'On cubic graphs having the maximum coalition number', Siberian Electronic Mathematical Reports, vol. 21, no. 1, pp. 363-369. https://doi.org/10.33048/semi.2024.21.027

APA

Dobrynin, A. A., & Golmohammadi, H. (2024). On cubic graphs having the maximum coalition number. Siberian Electronic Mathematical Reports, 21(1), 363-369. https://doi.org/10.33048/semi.2024.21.027

Vancouver

Dobrynin AA, Golmohammadi H. On cubic graphs having the maximum coalition number. Siberian Electronic Mathematical Reports. 2024;21(1):363-369. doi: 10.33048/semi.2024.21.027

Author

Dobrynin, A. A. ; Golmohammadi, H. / On cubic graphs having the maximum coalition number. In: Siberian Electronic Mathematical Reports. 2024 ; Vol. 21, No. 1. pp. 363-369.

BibTeX

@article{358c214b49ef432d8f718179352156e5,
title = "On cubic graphs having the maximum coalition number",
abstract = "A coalition in a graph G with a vertex set V consists of two disjoint sets V1, V2 ⊂ V, such that neither V1 nor V2 is a dominating set, but the union V1 ∪ V2 is a dominating set in G. A partition of graph vertices is called a coalition partition P if every non-dominating set of P is a member of a coalition, and every dominating set is a single-vertex set. The coalition number C(G) of a graph G is the maximum cardinality of its coalition partitions. It is known that for cubic graphs C(G) ≤ 9. The existence of cubic graphs with the maximum coalition number is an unsolved problem. In this paper, an in nite family of cubic graphs satisfying C(G) = 9 is constructed.",
keywords = "coalition number, cubic graph, dominating set",
author = "Dobrynin, {A. A.} and H. Golmohammadi",
note = "The study of A.A. Dobrynin was supported by the state contract of the Sobolev Institute of Mathematics (project number FWNF-2022-0017) and the work of Hamidreza Golmohammadi was supported by the Mathematical Center in Akademgorodok, under agreement No. 075-15-2022-281 with the Ministry of Science and High Education of the Russian Federation.",
year = "2024",
doi = "10.33048/semi.2024.21.027",
language = "English",
volume = "21",
pages = "363--369",
journal = "Сибирские электронные математические известия",
issn = "1813-3304",
publisher = "Sobolev Institute of Mathematics",
number = "1",

}

RIS

TY - JOUR

T1 - On cubic graphs having the maximum coalition number

AU - Dobrynin, A. A.

AU - Golmohammadi, H.

N1 - The study of A.A. Dobrynin was supported by the state contract of the Sobolev Institute of Mathematics (project number FWNF-2022-0017) and the work of Hamidreza Golmohammadi was supported by the Mathematical Center in Akademgorodok, under agreement No. 075-15-2022-281 with the Ministry of Science and High Education of the Russian Federation.

PY - 2024

Y1 - 2024

N2 - A coalition in a graph G with a vertex set V consists of two disjoint sets V1, V2 ⊂ V, such that neither V1 nor V2 is a dominating set, but the union V1 ∪ V2 is a dominating set in G. A partition of graph vertices is called a coalition partition P if every non-dominating set of P is a member of a coalition, and every dominating set is a single-vertex set. The coalition number C(G) of a graph G is the maximum cardinality of its coalition partitions. It is known that for cubic graphs C(G) ≤ 9. The existence of cubic graphs with the maximum coalition number is an unsolved problem. In this paper, an in nite family of cubic graphs satisfying C(G) = 9 is constructed.

AB - A coalition in a graph G with a vertex set V consists of two disjoint sets V1, V2 ⊂ V, such that neither V1 nor V2 is a dominating set, but the union V1 ∪ V2 is a dominating set in G. A partition of graph vertices is called a coalition partition P if every non-dominating set of P is a member of a coalition, and every dominating set is a single-vertex set. The coalition number C(G) of a graph G is the maximum cardinality of its coalition partitions. It is known that for cubic graphs C(G) ≤ 9. The existence of cubic graphs with the maximum coalition number is an unsolved problem. In this paper, an in nite family of cubic graphs satisfying C(G) = 9 is constructed.

KW - coalition number

KW - cubic graph

KW - dominating set

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85204484688&origin=inward

UR - https://www.mendeley.com/catalogue/44f69f0d-1fe6-3e94-bb26-b3f066cd53d4/

U2 - 10.33048/semi.2024.21.027

DO - 10.33048/semi.2024.21.027

M3 - Article

VL - 21

SP - 363

EP - 369

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

IS - 1

ER -

ID: 60559724