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Total coalitions of cubic graphs of order at most 10 | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 8، دوره 10، شماره 3، آذر 2025، صفحه 601-615 اصل مقاله (432.19 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.29015.1813 | ||
| نویسنده | ||
| Hamidreza Golmohammadi* 1، 2 | ||
| 1Novosibirsk State University, Pirogova str. 2, Novosibirsk, 630090, Russia | ||
| 2Sobolev Institute of Mathematics, Ak. Koptyug av. 4, Novosibirsk, 630090, Russia | ||
| چکیده | ||
| A total coalition in a graph $G=(V,E)$ consists of two disjoint sets of vertices $V_{1}$ and $V_{2}$, neither of which is a total dominating set but whose union $V_{1}\cup V_{2}$, is a total dominating set. A total coalition partition in a graph $G$ of order $n=|V|$ is a vertex partition $\tau = \{V_1, V_2, \dots , V_k \}$ such that every set $V_i \in \tau$ is not a total dominating set but forms a total coalition with another set $V_j\in \tau$ which is not a total dominating set. The total coalition number $TC(G)$ equals the maximum $k$ of a total coalition partition of $G$. In this paper, we determine the total coalition number of all cubic graphs of order $n \le 10$. | ||
| کلیدواژهها | ||
| Coalition؛ Total coalition؛ Cubic graphs | ||
| مراجع | ||
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