Coalition of cubic graphs of order at most 10

Coalition of cubic graphs of order at most 10 Full article

Journal

Communications in Combinatorics and Optimization
ISSN: 2538-2128 , E-ISSN: 2538-2136

Output data

Year: 2024, Volume: 9, Number: 3, Pages: 437-450 Pages count : 14 DOI: 10.22049/cco.2023.28328.1507

Tags

coalition; cubic graphs; Petersen graph

Authors

Alikhani Saeid ¹ , Golmohammadi Hamid Reza ^2,3 , Konstantinova Elena V. ^2,3

Affiliations

1	Department of Mathematical Sciences, Yazd University, 89195-741, Yazd, Iran
2	Novosibirsk State University, Pirogova str. 2, Novosibirsk, 630090, Russia
3	Sobolev Institute of Mathematics, Ak. Koptyug av. 4, Novosibirsk, 630090, Russia

Funding (1)

Russian Science Foundation

23-21-00459

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 number of all cubic graphs of order at most 10.

Alikhani S. , Golmohammadi H.R. , Konstantinova E.V.
Coalition of cubic graphs of order at most 10
Communications in Combinatorics and Optimization. 2024. V.9. N3. P.437-450. DOI: 10.22049/cco.2023.28328.1507 WOS Scopus

Submitted:	Feb 17, 2023
Accepted:	Apr 6, 2023
Published online:	Apr 10, 2023
Published print:	Jun 24, 2024

Web of science:	WOS:000967924600001
Scopus:	2-s2.0-85195019633

DB	Citing
Web of science	4
Scopus	8