On independent coalition in graphs and independent coalition graphs

On independent coalition in graphs and independent coalition graphs Full article

Journal

Discussiones Mathematicae - Graph Theory
ISSN: 1234-3099 , E-ISSN: 2083-5892

Output data

Year: 2025, Volume: 45, Number: 2, Pages: 533-544 Pages count : 12 DOI: 10.7151/dmgt.2543

Tags

dominating set, independent set, independent coalition, independent coalition number, independent coalition graph

Authors

Alikhani Saeid ¹ , Bakhshesh Davood ² , Golmohammadi Hamidreza ^3,4 , Klavžar Sandi ^5,6,7

Affiliations

1	Department of Mathematical Sciences, Yazd University
2	Department of Computer Science, University of Bojnord
3	Novosibirsk State University
4	Sobolev Institute of Mathematics
5	Faculty of Mathematics and Physics, University of Ljubljana
6	Institute of Mathematics, Physics and Mechanics
7	Faculty of Natural Sciences and Mathematics, University of Maribor

Funding (1)

Russian Science Foundation

23-21-00459

An independent coalition in a graph G consists of two disjoint, independent vertex sets V1 and V2, such that neither V1 nor V2 is a dominating set, but the union V1 V2 is an independent dominating set of G. An independent coalition partition of G is a partition V1 Vk of V(G) such that for every i [k], either the set Vi consists of a single dominating vertex of G, or Vi forms an independent coalition with some other part Vj. The independent coalition number IC(G) of G is the maximum order of an independent coalition of G. The independent coalition graph ICG(G ) of = V1 Vk (andofG)hasthe vertex set V1 Vk , vertices Vi and Vj being adjacent if Vi and Vj form an independent coalition in G. In this paper, a large family of graphs with IC(G) = 0 is described and graphs2 S. Alikhani, D. Bakhshesh, H.R. Golmohammadi and S. Klavzar G with IC(G) n(G)n(G) 1 are characterized. Some properties of ICG(G ) are presented. The independent coalition graphs of paths are characterized, and the independent coalition graphs of cycles described.

Alikhani S. , Bakhshesh D. , Golmohammadi H. , Klavžar S.
On independent coalition in graphs and independent coalition graphs
Discussiones Mathematicae - Graph Theory. 2025. V.45. N2. P.533-544. DOI: 10.7151/dmgt.2543 WOS Scopus РИНЦ OpenAlex

Submitted:	Oct 10, 2023
Accepted:	Mar 8, 2024
Published online:	Mar 25, 2024
Published print:	Apr 14, 2025

Web of science:	WOS:001511200100006
Scopus:	2-s2.0-105003041128
Elibrary:	66714256
OpenAlex:	W4393147505

DB	Citing
OpenAlex	2
Scopus	2