Total restrained coalitions in graphs

Total restrained coalitions in graphs Full article

Journal

Computational and Applied Mathematics
ISSN: 2238-3603 , E-ISSN: 1807-0302

Output data

Year: 2026, Volume: 45, Article number : 50, Pages count : DOI: 10.1007/s40314-025-03439-w

Tags

Coalition · Total restrained coalition · Total restrained dominating set

Authors

Golmohammadi H ^2,3,4 , Chellali M. ¹ , Matrokhin N.A. ² , Takhonov I.I. ² , Valenzuela-Tripodoro J.C. ⁵

Affiliations

1	LAMDA-ROLaboratory, Department of Mathematics, University of Blida, Blida, Algeria
2	Novosibirsk State University
3	Siberian State University of Telecommunications and Information Sciences
4	Sobolev Institute of Mathematics
5	Department of Mathematics, University of Cádiz, Cádiz, Spain

Funding (1)

Sobolev Institute of Mathematics

FWNF-2022-0017

Avertex set in a graph without isolated vertices is a total restrained dominating set (TRDset) if it is dominating, induces a subgraph without isolated vertices, and the vertices not in the set also induce a subgraph without isolated vertices. Two vertex sets, which are not TRD-sets, form a total restrained coalition if their union is a TRD-set. A total restrained coalition partition is a partition where none of its elements are TRD-sets, but each forms a total restrained coalition with another element. The goal is to maximize the cardinality of such a partition, denoted Ctr(G). We initiate the study of this concept by proving certain properties, extremal values, general bounds, and its relation to known structural parameters. Exact values for specific graph families are also provided.

Golmohammadi H. , Chellali M. , Matrokhin N.A. , Takhonov I.I. , Valenzuela-Tripodoro J.C.
Total restrained coalitions in graphs
Computational and Applied Mathematics. 2026. V.45. 50 . DOI: 10.1007/s40314-025-03439-w Scopus

Submitted:	Mar 11, 2025
Accepted:	Sep 8, 2025
Published online:	Oct 15, 2025

Scopus:

2-s2.0-105018820469

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