@article {
author = {Alikhani, Saeid and Golmohammadi, Hamidreza and Konstantinova, Elena},
title = {Coalition of cubic graphs of order at most $10$},
journal = {Communications in Combinatorics and Optimization},
volume = {9},
number = {3},
pages = {437-450},
year = {2024},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2023.28328.1507},
abstract = {The coalition in a graph $G$ consists of two disjoint sets of vertices $V_{1}$ and $V_{2}$, neither of which is a dominating set but whose union $V_{1}\cup V_{2}$, is a dominating set. A coalition partition in a graph $G$ is a vertex partition $\pi$ = $\{V_1, V_2,\dots, V_k \}$ such that every set $V_i \in \pi$ is not a dominating set but forms a coalition with another set $V_j\in \pi$ which is not a dominating set. The coalition number $C(G)$ equals the maximum $k$ of a coalition partition of $G$. In this paper, we compute the coalition numbers of all cubic graphs of order at most $10$.},
keywords = {Coalition,cubic graphs,Petersen graph},
url = {http://comb-opt.azaruniv.ac.ir/article_14542.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_14542_103d8d93afd44cc6d45e68bdcf8227d1.pdf}
}