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In this paper, we propose and investigate the concept of $k$-coalitions in graphs, where $k\ge 1$ is an integer. A $k$-coalition refers to a pair of disjoint vertex sets that jointly constitute a $k$-dominating set of the graph, meaning that every ve
Externí odkaz:
http://arxiv.org/abs/2407.09332
A subset of vertices $S$ of a graph $G$ is a dominating set if every vertex in $V \setminus S$ has at least one neighbor in $S$. A domatic partition is a partition of the vertices of a graph $G$ into disjoint dominating sets. The domatic number $d(G)
Externí odkaz:
http://arxiv.org/abs/2407.00103
Autor:
Bakhshesh, Davood, Henning, Michael A.
A set $S$ of vertices in a graph $G$ is a dominating set if every vertex of $V(G) \setminus S$ is adjacent to a vertex in $S$. A coalition in $G$ consists of two disjoint sets of vertices $X$ and $Y$ of $G$, neither of which is a dominating set but w
Externí odkaz:
http://arxiv.org/abs/2307.01222
Let $G$ be graph with vertex set $V$ and order $n=|V|$. A coalition in $G$ is a combination of two distinct sets, $A\subseteq V$ and $B\subseteq V$, which are disjoint and are not dominating sets of $G$, but $A\cup B$ is a dominating set of $G$. A co
Externí odkaz:
http://arxiv.org/abs/2304.07606
The connected coalition in a graph $G=(V,E)$ consists of two disjoint sets of vertices $V_{1}$ and $V_{2}$, neither of which is a connected dominating set but whose union $V_{1}\cup V_{2}$, is a connected dominating set. A connected coalition partiti
Externí odkaz:
http://arxiv.org/abs/2302.05754
Let $G$ be a graph with vertex set $V$. Two disjoint sets $V_1, V_2\subseteq V$ are called a total coalition in $G$, if neither $V_1$ and $V_2$ is a total dominating set of $G$ but $V_1\cup V_2$ is a total dominating set. A total coalition partition
Externí odkaz:
http://arxiv.org/abs/2211.11590
Let $G$ be a graph with vertex set $V$ and of order $n = |V|$, and let $\delta(G)$ and $\Delta(G)$ be the minimum and maximum degree of $G$, respectively. Two disjoint sets $V_1, V_2 \subseteq V$ form a coalition in $G$ if none of them is a dominatin
Externí odkaz:
http://arxiv.org/abs/2111.08945
Akademický článek
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Let $G=(V, E)$ be a simple and undirected graph. For some integer $k\geq 1$, a set $D\subseteq V$ is said to be a k-dominating set in $G$ if every vertex $v$ of $G$ outside $D$ has at least $k$ neighbors in $D$. Furthermore, for some real number $\al
Externí odkaz:
http://arxiv.org/abs/1702.00533
Autor:
Bakhshesh, Davood, Farshi, Mohammad
Publikováno v:
In Computational Geometry: Theory and Applications January 2022 100
