Work

Strong coalitions in graphs

Year: 2026

Type: article

Abstract: For a graph [Formula: see text], a set [Formula: see text] is a strong dominating set of [Formula: see text], if for every vertex [Formula: see text] there is a vertex [Formula: see text] with [Formula: see text] and [Formula: see text]. A strong coalition consists of two disjoint sets of vertices [Formula: see text] and [Formula: see text], neither of which is a strong dominating set but whose union [Formula: see text] is a strong dominating set. A vertex partition [Formula: see text] of vertices in [Formula: see text] is a strong coalition partition if every set [Formula: see text] either is a strong dominating set consisting of a single vertex of degree [Formula: see text], or is not a strong dominating set but forms a strong coalition with another set [Formula: see text] that is not a strong dominating set. In this paper, we study properties of strong coalitions in graphs.

Source: Discrete Mathematics Algorithms and Applications

DOI: 10.1142/s1793830926500850

Authors: H. Golmohammadi, S. Alikhani, N. Ghanbari, I. I. Takhonov, A. Abaturov

Institutions: Novosibirsk State University, Sobolev Institute of Mathematics, Siberian State University of Telecommunications and Information Science, Yazd University

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4394948172

FWCI:

Cites:

Cited by: 1

Related to: 10