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pro vyhledávání: '"05C78, 05C15"'
A graph has a locating rainbow coloring if every pair of its vertices can be connected by a path passing through internal vertices with distinct colors and every vertex generates a unique rainbow code. The minimum number of colors needed for a graph
Externí odkaz:
http://arxiv.org/abs/2410.09304
Autor:
Lau, Gee-Choon
Let $G = (V,E)$ be a connected simple graph of order $p$ and size $q$. A bijection $f:V(G)\cup E(G)\to \{1,2,\ldots,p+q\}$ is called a local antimagic total labeling of $G$ if for any two adjacent vertices $u$ and $v$, we have $w(u)\ne w(v)$, where $
Externí odkaz:
http://arxiv.org/abs/2407.14113
Frank Harary introduced the concepts of sum and integral sum graphs. A graph $G$ is a \textit{sum graph} if the vertices of $G$ can be labeled with distinct positive integers so that $e = uv$ is an edge of $G$ if and only if the sum of the labels on
Externí odkaz:
http://arxiv.org/abs/2407.10917
Autor:
Vasoya, Payal, Bantva, Devsi
A radio labelling of a graph $G$ is a mapping $f : V(G) \rightarrow \{0, 1, 2,\ldots\}$ such that $|f(u)-f(v)|\geq diam(G) + 1 - d(u,v)$ for every pair of distinct vertices $u,v$ of $G$, where $diam(G)$ is the diameter of $G$ and $d(u,v)$ is the dist
Externí odkaz:
http://arxiv.org/abs/2404.08400
The locating rainbow connection number of a graph is defined as the minimum number of colors required to color vertices such that every two vertices there exists a rainbow vertex path and every vertex has a distinct rainbow code. This rainbow code si
Externí odkaz:
http://arxiv.org/abs/2403.06004
Autor:
Vasoya, Payal, Bantva, Devsi
Publikováno v:
Discrete Mathematics, Algorithms and Applications, 2024
A radio labeling of a graph $G$ is a function $f : V(G) \rightarrow \{0,1,2,\ldots\}$ such that $|f(u)-f(v)| \geq diam(G) + 1 - d(u,v)$ for every pair of distinct vertices $u,v$ of $G$. The radio number of $G$, denoted by $rn(G)$, is the smallest num
Externí odkaz:
http://arxiv.org/abs/2304.10094
Autor:
Bantva, Devsi, Vihol, P L
For a simple finite connected graph $G$, let $diam(G)$ and $d_{G}(u,v)$ denote the diameter of $G$ and distance between $u$ and $v$ in $G$, respectively. A radio labeling of a graph $G$ is a mapping $f$ : $V(G) \rightarrow \{0, 1, 2,...\}$ such that
Externí odkaz:
http://arxiv.org/abs/2303.06432
Autor:
Bantva, Devsi
Let $\mathbb{N}$ be the set of positive integers. A radio labeling of a graph $G$ is a mapping $\varphi : V(G) \rightarrow \mathbb{N} \cup \{0\}$ such that the inequality $|\varphi(u)-\varphi(v)| \geq diam(G) + 1 - d(u,v)$ holds for every pair of dis
Externí odkaz:
http://arxiv.org/abs/2212.13578
Autor:
Kamalappan, V. Vilfred
We define a labeling $f:$ $V(G)$ $\rightarrow$ $\{1, 2, \ldots, n\}$ on a graph $G$ of order $n \geq 3$ as a \emph{$k$-distance magic} ($k$-DM) if $\sum_{w\in \partial N_k(u)}{ f(w)}$ is a constant and independent of $u\in V(G)$ where $\partial N_k(u
Externí odkaz:
http://arxiv.org/abs/2211.09666
Autor:
Lau, Gee-Choon, Nalliah, M.
In this paper, we provide a correct proof for the lower bounds of the local antimagic chromatic number of the corona product of friendship and fan graphs with null graph respectively as in [On local antimagic vertex coloring of corona products relate
Externí odkaz:
http://arxiv.org/abs/2203.09906