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pro vyhledávání: '"Henning, Michael"'
Let $p \in \mathbb{N}$ and $q \in \mathbb{N} \cup \lbrace \infty \rbrace$. We study a dynamic coloring of the vertices of a graph $G$ that starts with an initial subset $S$ of blue vertices, with all remaining vertices colored white. If a white verte
Externí odkaz:
http://arxiv.org/abs/2411.14889
The balance game is played on a graph $G$ by two players, Admirable (A) and Impish (I), who take turns selecting unlabeled vertices of $G$. Admirable labels the selected vertices by $0$ and Impish by $1$, and the resulting label on any edge is the su
Externí odkaz:
http://arxiv.org/abs/2409.01796
An identifying open code of a graph $G$ is a set $S$ of vertices that is both a separating open code (that is, $N_G(u) \cap S \ne N_G(v) \cap S$ for all distinct vertices $u$ and $v$ in $G$) and a total dominating set (that is, $N(v) \cap S \ne \empt
Externí odkaz:
http://arxiv.org/abs/2407.09692
In network theory, the domination parameter is vital in investigating several structural features of the networks, including connectedness, their tendency to form clusters, compactness, and symmetry. In this context, various domination parameters hav
Externí odkaz:
http://arxiv.org/abs/2407.01935
Autor:
Henning, Michael A., Topp, Jerzy
A set $S$ of vertices in a graph $G$ is a total dominating set of $G$ if every vertex is adjacent to a vertex in $S$. The total domination number $\gamma_t(G)$ is the minimum cardinality of a total dominating set of $G$. The total domination subdivis
Externí odkaz:
http://arxiv.org/abs/2404.16186
An $\textit{identifying code}$ of a closed-twin-free graph $G$ is a set $S$ of vertices of $G$ such that any two vertices in $G$ have a distinct intersection between their closed neighborhood and $S$. It was conjectured that there exists a constant $
Externí odkaz:
http://arxiv.org/abs/2403.17877
Autor:
Brešar, Boštjan, Henning, Michael A.
A dominating set in a graph $G$ is a set $S$ of vertices such that every vertex in $V(G) \setminus S$ is adjacent to a vertex in $S$. A restrained dominating set of $G$ is a dominating set $S$ with the additional restraint that the graph $G - S$ obta
Externí odkaz:
http://arxiv.org/abs/2403.17129
An $\textit{identifying code}$ of a closed-twin-free graph $G$ is a dominating set $S$ of vertices of $G$ such that any two vertices in $G$ have a distinct intersection between their closed neighborhoods and $S$. It was conjectured that there exists
Externí odkaz:
http://arxiv.org/abs/2403.13172
Autor:
Dorbec, Paul, Henning, Michael Antony
A set S of vertices in a graph G is a dominating set of G if every vertex not in S is adjacent to a vertex in S . The domination number of G, denoted by $\gamma$(G), is the minimum cardinality of a dominating set in G. In a breakthrough paper in 2008
Externí odkaz:
http://arxiv.org/abs/2401.17820
In this follow-up to [M.G.~Cornet, P.~Torres, arXiv:2308.15603], where the $k$-tuple domination number and the 2-packing number in Kneser graphs $K(n,r)$ were studied, we are concerned with two variations, the $k$-domination number, ${\gamma_{k}}(K(n
Externí odkaz:
http://arxiv.org/abs/2312.15464