Zobrazeno 1 - 10
of 38
pro vyhledávání: '"05C78, 05C69"'
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
Autor:
Lau, Gee-Choon, Shiu, Wai Chee
For a graph $G(V,E)$ of size $q$, a bijection $f : E(G) \to [1,q]$ is a local antimagc labeling if it induces a vertex labeling $f^+ : V(G) \to \mathbb{N}$ such that $f^+(u) \ne f^+(v)$, where $f^+(u)$ is the sum of all the incident edge label(s) of
Externí odkaz:
http://arxiv.org/abs/2408.06703
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 use matrices of size $(2m+1) \times (2k+1)$ to completely determine the local antimagic chromatic number of the
Externí odkaz:
http://arxiv.org/abs/2408.04942
An edge labeling of a connected graph $G = (V, E)$ is said to be local antimagic if it is a bijection $f:E \to\{1,\ldots ,|E|\}$ such that for any pair of adjacent vertices $x$ and $y$, $f^+(x)\not= f^+(y)$, where the induced vertex label $f^+(x)= \s
Externí odkaz:
http://arxiv.org/abs/2404.18049
An edge labeling of a connected graph $G = (V, E)$ is said to be local antimagic if there is a bijection $f:E \to\{1,\ldots ,|E|\}$ such that for any pair of adjacent vertices $x$ and $y$, $f^+(x)\not= f^+(y)$, where the induced vertex label $f^+(x)=
Externí odkaz:
http://arxiv.org/abs/2403.16484
Autor:
Lau, G. C.
A total labeling of a graph $G = (V, E)$ is said to be local total antimagic if it is a bijection $f: V\cup E \to\{1,\ldots ,|V|+|E|\}$ such that adjacent vertices, adjacent edges, and incident vertex and edge have distinct induced weights where the
Externí odkaz:
http://arxiv.org/abs/2401.14653
Let $G$ be a simple graph of order $n$. A majority dominator coloring of a graph $G$ is proper coloring in which each vertex of the graph dominates at least half of one color class. The majority dominator chromatic number $\chi_{md}(G)$ is the minimu
Externí odkaz:
http://arxiv.org/abs/2212.14082
An edge labeling of a connected graph $G = (V, E)$ is said to be local antimagic if it is a bijection $f:E \to\{1,\ldots ,|E|\}$ such that for any pair of adjacent vertices $x$ and $y$, $f^+(x)\not= f^+(y)$, where the induced vertex label $f^+(x)= \s
Externí odkaz:
http://arxiv.org/abs/2210.04394
Autor:
Pokrovskiy, Alexey
Recently Lau-Jeyaseeli-Shiu-Arumugam introduced the concept of the "Sudoku colourings" of graphs -- partial $\chi(G)$-colourings of $G$ that have a unique extension to a proper $\chi(G)$-colouring of all the vertices. They introduced the Sudoku numbe
Externí odkaz:
http://arxiv.org/abs/2206.08914
We introduce a new concept in graph coloring motivated by the popular Sudoku puzzle. Let $G=(V,E)$ be a graph of order $n$ with chromatic number $\chi(G)=k$ and let $S\subseteq V.$ Let $\mathscr C_0$ be a $k$-coloring of the induced subgraph $G[S].$
Externí odkaz:
http://arxiv.org/abs/2206.08106