Zobrazeno 1 - 10
of 2 964
pro vyhledávání: '"05c69"'
A dominating set $D_{f}\subseteq V(G)$ of vertices in a graph $G$ is called a \emph{dom-forcing set} if the sub-graph induced by $\langle D_{f} \rangle$ must form a zero forcing set. The minimum cardinality of such a set is known as the dom-forcing n
Externí odkaz:
http://arxiv.org/abs/2411.00580
Let $G$ be a simple graph. A dissociation set of $G$ is defined as a set of vertices that induces a subgraph in which every vertex has a degree of at most 1. A dissociation set is maximal if it is not contained as a proper subset in any other dissoci
Externí odkaz:
http://arxiv.org/abs/2410.20462
Autor:
Galvin, David, Marmorino, Phillip
An $n$-vertex, $d$-regular graph can have at most $2^{n/2+o_d(n)}$ independent sets. In this paper we address what happens with this upper bound when we impose the further condition that the graph has independence number at most $\alpha$. We give upp
Externí odkaz:
http://arxiv.org/abs/2410.19959
We prove that a hereditary class of graphs is $(\mathsf{tw}, \omega)$-bounded if and only if the induced minors of the graphs from the class form a $(\mathsf{tw}, \omega)$-bounded class.
Externí odkaz:
http://arxiv.org/abs/2410.17979
Autor:
Lau, Gee-Choon, Shiu, Wai Chee
It is known that null graphs and 1-regular graphs are the only regular graphs without local antimagic chromatic number. In this paper, we proved that the join of 1-regular graph and a null graph has local antimagic chromatic number is 3. Consequently
Externí odkaz:
http://arxiv.org/abs/2410.17674
The energy $En(G)$ of a graph $G$ is defined as the sum of the absolute values of its eigenvalues. The Hosoya index $Z(G)$ of a graph $G$ is the number of independent edge subsets of $G$, including the empty set. For any given degree sequence $D$, we
Externí odkaz:
http://arxiv.org/abs/2410.16810
Zero forcing is a graph propagation process for which vertices fill-in (or propagate information to) neighbor vertices if all neighbors except for one, are filled. The zero-forcing number is the smallest number of vertices that must be filled to begi
Externí odkaz:
http://arxiv.org/abs/2410.17440
A biclique in a graph $G$ is a complete bipartite subgraph (not necessarily induced), and the least positive integer $k$ for which the vertex set of $G$ can be partitioned into at most $k$ bicliques is the biclique vertex partition number $bp(G)$ of
Externí odkaz:
http://arxiv.org/abs/2410.15213
Autor:
Kostyukova, O. I., Tchemisova, T. V.
There is a profound connection between copositive matrices and graph theory. Copositive matrices provide a powerful tool for formulating and solving various challenging graph-related problems. Conversely, graph theory provides a rich set of concepts
Externí odkaz:
http://arxiv.org/abs/2410.08066
Autor:
Mella, Lorenzo, Pasotti, Anita
In this paper we introduce a new domination problem strongly related to the following one recently proposed by Broe, Chartrand and Zhang. One says that a vertex $v$ of a graph $\Gamma$ labeled with an integer $\ell$ dominates the vertices of $\Gamma$
Externí odkaz:
http://arxiv.org/abs/2410.04782