Strong coalitions in graphs | Sciact

Strong coalitions in graphs Full article

Journal

Discrete Mathematics, Algorithms and Applications
ISSN: 1793-8309

Output data

Year: 2026, Pages: 1-15 Pages count : 15 DOI: 10.1142/S1793830926500850

Tags

Coalition, strong dominating set, strong coalition

Authors

Golmohammadi H. ^1,2 , Alikhani S. ³ , Ghanbari N. ³ , Takhonov I.I. ¹ , Abaturov A. ¹

Affiliations

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

Funding (1)

Министерство науки и высшего образования РФ

075-15-2025-348

For a graph G = (V, E), a set D ⊂ V (G) is a strong dominating set of G,if for every vertex x ∈ V (G) \ D there is a vertex y ∈ D with xy ∈ E(G) and deg(x) ≤ deg(y). A strong coalition consists of two disjoint sets of vertices V1 and V2, neither of which is a strong dominating set but whose union V1 ∪ V2 is a strong dominating set. A vertex partition Ω = {V1, V2, ..., Vk} of vertices in G is a strong coalition partition if every set Vi ∈ Ω either is a strong dominating set consisting of a single vertex of degree n − 1, or is not a strong dominating set but forms a strong coalition with another set Vj ∈ Ω that is not a strong dominating set. In this paper, we study properties of strong coalitions in graphs.

Golmohammadi H. , Alikhani S. , Ghanbari N. , Takhonov I.I. , Abaturov A.
Strong coalitions in graphs
Discrete Mathematics, Algorithms and Applications. 2026. P.1-15. DOI: 10.1142/S1793830926500850 OpenAlex

Submitted:	Jul 31, 2025
Accepted:	Aug 12, 2026
Published online:	Aug 28, 2026

≡ OpenAlex:

W4394948172