Total coalitions in graphs | Sciact

Total coalitions in graphs Full article

Journal

Quaestiones Mathematicae
ISSN: 1607-3606

Output data

Year: 2024, Volume: 47, Number: 11, Pages: 2283-2294 Pages count : 12 DOI: 10.2989/16073606.2024.2365365

Tags

Total dominating set, coalition, total coalition, tree

Authors

Alikhani Saeid ¹ , Bakhshesh Davood ² , Golmohammadi Hamidreza ^3,4

Affiliations

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

We define a total coalition in a graph G as a pair of disjoint subsets A1,A2 ⊆ A that satisfy the following conditions: (a) neither A1 nor A2 constitutes a total dominating set of G, and (b) A1 ∪ A2 constitutes a total dominating set of G. A total coalition partition of a graph G is a partition ϒ = {A1,A2, . . . ,Ak} of its vertex set such that no subset of ϒ acts as a total dominating set of G, but for every set Ai ∈ ϒ, there exists a set Aj ∈ ϒ such that Ai and Aj combine to form a total coalition. We define the total coalition number of G as the maximum cardinality of a total coalition partition of G, and we denote it by Ct(G). The purpose of this paper is to begin an investigation into the characteristics of total coalition in graphs.

Alikhani S. , Bakhshesh D. , Golmohammadi H.
Total coalitions in graphs
Quaestiones Mathematicae. 2024. V.47. N11. P.2283-2294. DOI: 10.2989/16073606.2024.2365365 WOS Scopus OpenAlex

Submitted:	Dec 3, 2023
Published online:	Jul 7, 2024
Published print:	Dec 3, 2024

Web of science:	WOS:001264642200001
Scopus:	2-s2.0-85197702705
OpenAlex:	W4400427885

DB	Citing
OpenAlex	8
Scopus	10
Web of science	10