TY - JOUR
ID - 14542
TI - Coalition of cubic graphs of order at most $10$
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Alikhani, Saeid
AU - Golmohammadi, Hamidreza
AU - Konstantinova, Elena V.
AD - Department of Mathematical Sciences, Yazd University, 89195-741, Yazd, Iran
AD - Novosibirsk State University, Pirogova str. 2, Novosibirsk, 630090, Russia
Y1 - 2024
PY - 2024
VL - 9
IS - 3
SP - 437
EP - 450
KW - Coalition
KW - cubic graphs
KW - Petersen graph
DO - 10.22049/cco.2023.28328.1507
N2 - 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 $10$.
UR - http://comb-opt.azaruniv.ac.ir/article_14542.html
L1 - http://comb-opt.azaruniv.ac.ir/article_14542_103d8d93afd44cc6d45e68bdcf8227d1.pdf
ER -