TY - JOUR

T1 - Coalition of cubic graphs of order at most 10

AU - Alikhani, Saeid

AU - Голмохаммади, Хамидреза

AU - Константинова, Елена Валентиновна

N1 - The research by Hamidreza Golmohammadi and Elena V. Konstantinova was supported by the Russian Science Foundation under grant no. 23-21-00459.

PY - 2024/9

Y1 - 2024/9

N2 - The coalition in a graph G consists of two disjoint sets of vertices V1 and V2, neither of which is a dominating set but whose union V1 ∪ V2, is a dominating set. A coalition partition in a graph G is a vertex partition π={V1, V2, ..., Vk} such that every set Vi∈Π is not a dominating set but forms a coalition with another set Vj∈Π which is not a dominating set. The coalition number C(G) equals the maximum κ of a coalition partition of G. In this paper, we compute the coalition numbers of all cubic graphs of order at most 10.

AB - The coalition in a graph G consists of two disjoint sets of vertices V1 and V2, neither of which is a dominating set but whose union V1 ∪ V2, is a dominating set. A coalition partition in a graph G is a vertex partition π={V1, V2, ..., Vk} such that every set Vi∈Π is not a dominating set but forms a coalition with another set Vj∈Π which is not a dominating set. The coalition number C(G) equals the maximum κ of a coalition partition of G. In this paper, we compute the coalition numbers of all cubic graphs of order at most 10.

KW - coalition

KW - cubic graphs

KW - Petersen graph

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85195019633&origin=inward&txGid=8f13530b439bf419eeb17b0680f34a38

UR - https://www.mendeley.com/catalogue/5878cf63-5c82-3bf6-96e4-7a56f824795c/

U2 - 10.22049/CCO.2023.28328.1507

DO - 10.22049/CCO.2023.28328.1507

M3 - Article

VL - 9

SP - 437

EP - 450

JO - Communications in Combinatorics and Optimization

JF - Communications in Combinatorics and Optimization

SN - 2538-2128

IS - 3

ER -