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pro vyhledávání: '"Ismael G"'
Two relationships between the injective chromatic number and, respectively, chromatic number and chromatic index, are proved. They are applied to determine the injective chromatic number of Sierpi\'nski graphs and to give a short proof that Sierpi\'n
Externí odkaz:
http://arxiv.org/abs/2409.08856
Given a graph $G$, a mutual-visibility coloring of $G$ is introduced as follows. We color two vertices $x,y\in V(G)$ with a same color, if there is a shortest $x,y$-path whose internal vertices have different colors than $x,y$. The smallest number of
Externí odkaz:
http://arxiv.org/abs/2408.03132
The mutual-visibility problem in a graph $G$ asks for the cardinality of a largest set of vertices $S\subseteq V(G)$ so that for any two vertices $x,y\in S$ there is a shortest $x,y$-path $P$ so that all internal vertices of $P$ are not in $S$. This
Externí odkaz:
http://arxiv.org/abs/2401.02373
Let $G$ and $H$ be graphs and let $f \colon V(G)\rightarrow V(H)$ be a function. The Sierpi\'{n}ski product of $G$ and $H$ with respect to $f$, denoted by $G \otimes _f H$, is defined as the graph on the vertex set $V(G)\times V(H)$, consisting of $|
Externí odkaz:
http://arxiv.org/abs/2309.15196
The classical (vertex) metric dimension of a graph G is defined as the cardinality of a smallest set S in V (G) such that any two vertices x and y from G have different distances to least one vertex from S: The k-metric dimension is a generalization
Externí odkaz:
http://arxiv.org/abs/2309.00922
Autor:
Brešar, Boštjan, Yero, Ismael G.
Given a graph $G$, a set $X$ of vertices in $G$ satisfying that between every two vertices in $X$ (respectively, in $G$) there is a shortest path whose internal vertices are not in $X$ is a mutual-visibility (respectively, total mutual-visibility) se
Externí odkaz:
http://arxiv.org/abs/2307.02951
Publikováno v:
Bulletin of the Malaysian Mathematical Sciences Society, 2024
The problem of injective coloring in graphs can be revisited through two different approaches: coloring the two-step graphs and vertex partitioning of graphs into open packing sets, each of which is equivalent to the injective coloring problem itself
Externí odkaz:
http://arxiv.org/abs/2306.01488
Autor:
Cicerone, Serafino, Di Stefano, Gabriele, Drozek, Lara, Hedzet, Jaka, Klavzar, Sandi, Yero, Ismael G.
If $X$ is a subset of vertices of a graph $G$, then vertices $u$ and $v$ are $X$-visible if there exists a shortest $u,v$-path $P$ such that $V(P)\cap X \subseteq \{u,v\}$. If each two vertices from $X$ are $X$-visible, then $X$ is a mutual-visibilit
Externí odkaz:
http://arxiv.org/abs/2304.00864
This work focuses on the (k,l)-anonymity of some networks as a measure of their privacy against active attacks. Two different types of networks are considered. The first one consists of graphs with a predetermined structure, namely cylinders, toruses
Externí odkaz:
http://arxiv.org/abs/2304.00849
Autor:
Hakanen, Anni, Yero, Ismael G.
Publikováno v:
Fundamenta Informaticae, Volume 191, Issues 3-4: Iiro Honkala's 60 Birthday (November 10, 2024) fi:11068
This investigation is firstly focused into showing that two metric parameters represent the same object in graph theory. That is, we prove that the multiset resolving sets and the ID-colorings of graphs are the same thing. We also consider some compu
Externí odkaz:
http://arxiv.org/abs/2303.06986