Standard

Total coalitions of cubic graphs of order at most 10. / Голмохаммади, Хамидреза .

In: Communications in Combinatorics and Optimization, Vol. 10, No. 3, 2024, p. 601-615.

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

Harvard

Голмохаммади, Х 2024, 'Total coalitions of cubic graphs of order at most 10', Communications in Combinatorics and Optimization, vol. 10, no. 3, pp. 601-615. https://doi.org/10.22049/CCO.2024.29015.1813

APA

Голмохаммади, Х. (2024). Total coalitions of cubic graphs of order at most 10. Communications in Combinatorics and Optimization, 10(3), 601-615. https://doi.org/10.22049/CCO.2024.29015.1813

Vancouver

Голмохаммади Х. Total coalitions of cubic graphs of order at most 10. Communications in Combinatorics and Optimization. 2024;10(3):601-615. Epub 2024 Jan 30. doi: 10.22049/CCO.2024.29015.1813

Author

Голмохаммади, Хамидреза . / Total coalitions of cubic graphs of order at most 10. In: Communications in Combinatorics and Optimization. 2024 ; Vol. 10, No. 3. pp. 601-615.

BibTeX

@article{805f037f58c043f98f42a6b2549b3ae7,
title = "Total coalitions of cubic graphs of order at most 10",
abstract = "A total coalition in a graph G = (V, E) consists of two disjoint sets of vertices V1 and V2, neither of which is a total dominating set but whose union V1 ∪V2, is a total dominating set. A total coalition partition in a graph G of order n = |V | is a vertex partition τ = {V1, V2, . . ., Vk} such that every set Vi ∈ τ is not a total dominating set but forms a total coalition with another set Vj ∈ τ which is not a total dominating set. The total coalition number TC(G) equals the maximum order k of a total coalition partition of G. In this paper, we determine the total coalition number of all cubic graphs of order n ≤ 10.",
keywords = "Petersen graph, coalition, cubic graphs, total coalition",
author = "Хамидреза Голмохаммади",
year = "2024",
doi = "10.22049/CCO.2024.29015.1813",
language = "English",
volume = "10",
pages = "601--615",
journal = "Communications in Combinatorics and Optimization",
issn = "2538-2128",
publisher = "Azarbaijan Shahid Madani University",
number = "3",

}

RIS

TY - JOUR

T1 - Total coalitions of cubic graphs of order at most 10

AU - Голмохаммади, Хамидреза

PY - 2024

Y1 - 2024

N2 - A total coalition in a graph G = (V, E) consists of two disjoint sets of vertices V1 and V2, neither of which is a total dominating set but whose union V1 ∪V2, is a total dominating set. A total coalition partition in a graph G of order n = |V | is a vertex partition τ = {V1, V2, . . ., Vk} such that every set Vi ∈ τ is not a total dominating set but forms a total coalition with another set Vj ∈ τ which is not a total dominating set. The total coalition number TC(G) equals the maximum order k of a total coalition partition of G. In this paper, we determine the total coalition number of all cubic graphs of order n ≤ 10.

AB - A total coalition in a graph G = (V, E) consists of two disjoint sets of vertices V1 and V2, neither of which is a total dominating set but whose union V1 ∪V2, is a total dominating set. A total coalition partition in a graph G of order n = |V | is a vertex partition τ = {V1, V2, . . ., Vk} such that every set Vi ∈ τ is not a total dominating set but forms a total coalition with another set Vj ∈ τ which is not a total dominating set. The total coalition number TC(G) equals the maximum order k of a total coalition partition of G. In this paper, we determine the total coalition number of all cubic graphs of order n ≤ 10.

KW - Petersen graph

KW - coalition

KW - cubic graphs

KW - total coalition

UR - https://www.mendeley.com/catalogue/ab7549b6-cb1f-32b7-897e-72798f979ce0/

U2 - 10.22049/CCO.2024.29015.1813

DO - 10.22049/CCO.2024.29015.1813

M3 - Article

VL - 10

SP - 601

EP - 615

JO - Communications in Combinatorics and Optimization

JF - Communications in Combinatorics and Optimization

SN - 2538-2128

IS - 3

ER -

ID: 59879950