Standard

Total coalitions in graphs. / Alikhani, Saeid; Bakhshesh, Davood; Golmohammadi, Hamidreza.

In: Quaestiones Mathematicae, 2024.

Research output: Contribution to journal › Article › peer-review

Harvard

Alikhani, S, Bakhshesh, D & Golmohammadi, H 2024, 'Total coalitions in graphs', Quaestiones Mathematicae. https://doi.org/10.2989/16073606.2024.2365365

APA

Alikhani, S., Bakhshesh, D., & Golmohammadi, H. (2024). Total coalitions in graphs. Quaestiones Mathematicae. https://doi.org/10.2989/16073606.2024.2365365

Vancouver

Alikhani S, Bakhshesh D, Golmohammadi H. Total coalitions in graphs. Quaestiones Mathematicae. 2024. doi: 10.2989/16073606.2024.2365365

Author

Alikhani, Saeid ; Bakhshesh, Davood ; Golmohammadi, Hamidreza. / Total coalitions in graphs. In: Quaestiones Mathematicae. 2024.

BibTeX

@article{956c2468c0914247863bb94cad2dfd1f,
title = "Total coalitions in graphs",
abstract = "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.",
keywords = "Total dominating set, coalition, total coalition, tree",
author = "Saeid Alikhani and Davood Bakhshesh and Hamidreza Golmohammadi",
year = "2024",
doi = "10.2989/16073606.2024.2365365",
language = "English",
journal = "Quaestiones Mathematicae",
issn = "1727-933X",
publisher = "Taylor and Francis Ltd.",

}

RIS

TY - JOUR

T1 - Total coalitions in graphs

AU - Alikhani, Saeid

AU - Bakhshesh, Davood

AU - Golmohammadi, Hamidreza

PY - 2024

Y1 - 2024

N2 - 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.

AB - 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.

KW - Total dominating set

KW - coalition

KW - total coalition

KW - tree

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85197702705&origin=inward&txGid=edc64a075e14e73cb00b658beb736117

UR - https://www.mendeley.com/catalogue/c6cbdc90-7ab7-30bf-8b66-57eccda6ed60/

U2 - 10.2989/16073606.2024.2365365

DO - 10.2989/16073606.2024.2365365

M3 - Article

JO - Quaestiones Mathematicae

JF - Quaestiones Mathematicae

SN - 1727-933X

ER -

ID: 60535109