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Coalition graphs of connected domination partitions in subcubic graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 2، دوره 12، شماره 1، خرداد 2027، صفحه 17-32 اصل مقاله (493.53 K) | ||
| نوع مقاله: Special issue of CCO to honor Odile Favaron | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.31013.2710 | ||
| نویسندگان | ||
| Andrey A. Dobrynin* ؛ Aleksey N. Glebov | ||
| Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 630090, Russia | ||
| چکیده | ||
| A graph is subcubic if it is connected and its maximum vertex degree does not exceed 3. Two disjoint vertex subsets of a graph $G$ form a connected coalition in $G$ if neither of them is a connected dominating set but their union is a connected dominating set. A connected coalition partition of $G$ is a partition of its vertices $\pi(G) = \{V_1, V_2,..., V_k \}$, such that each $V_i$ is either a connected dominating set consisting of a single vertex or forms a coalition with some set of $\pi(G)$. The formation of connected coalitions is described by a coalition graph whose vertices correspond to the sets of $\pi$, and two vertices are adjacent if and only if the corresponding sets form a coalition in $G$. We characterize all coalition graphs of subcubic graphs. | ||
| کلیدواژه‌ها | ||
| domination؛ coalition partition؛ coalition graph؛ subcubic graph | ||
| مراجع | ||
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