Results 21 to 30 of about 19,166,067 (60)
Super Total Local Antimagic Vertex Coloring of Graphs
, 2023 Let $G = (V,E)$ be a finite simple undirected graph without isolated vertices. A bijective map $f: V \cup E \rightarrow \{1,2, \dots, |V|+ |E| \}$ is called total local antimagic labeling if for each edge $uv \in E, w(u) \ne w(v)$, where $w(v)$ is a ...
Pawar, Ravindra, Singh, Tarkeshwar
core +1 more source
On bridge graphs with local antimagic chromatic number 3
, 2023 Let $G=(V, E)$ be a connected graph. A bijection $f: E\to \{1, \ldots, |E|\}$ is called a local antimagic labeling if for any two adjacent vertices $x$ and $y$, $f^+(x)\neq f^+(y)$, where $f^+(x)=\sum_{e\in E(x)}f(e)$ and $E(x)$ is the set of edges ...
Lau, G. C., Shiu, W. C., Zhang, R. X.
core
On local antimagic chromatic numbers of circulant graphs join with null graphs or cycles
, 2023 An edge labeling of a graph G = (V,E) is said to be local antimagic if there is a bijection f : E → {1,..., |E|} such that for any pair of adjacent vertices x and y, f +(x) ≠ f +(y), where the induced vertex label is f +(x) = ?
G. C. Lau +8 more
core +1 more source
Local Antimagic Coloring of Some Graphs [PDF]
, 2023 Given a graph $G =(V,E)$, a bijection $f: E \rightarrow \{1, 2, \dots,|E|\}$ is called a local antimagic labeling of $G$ if the vertex weight $w(u) = \sum_{uv \in E} f(uv)$ is distinct for all adjacent vertices.
Pawar, Ravindra +3 more
core +1 more source
A note on local edge antimagic chromatic number of graphs
Let $G$ be a finite, undirected and simple graph. A bijection $f : V(G) \to [1,|V(G)|]$ is called a local edge antimagic labeling if for any two adjacent edges $uv,vw \in E(G), f(u) \ne f(w)$.
Maryati, Tita Khalis +1 more
core +1 more source
The harmonious chromatic number of almost all trees [PDF]
, 1995 A harmonious colouring of a simple graph G is a proper vertex colouring such that each pair of colours appears together on at most one edge. The harmonious chromatic number h(G) is the least number of colours in such a colouring.For any positive integer ...
Edwards, Keith
core +1 more source
On local antimagic chromatic number of the join of two special families of graphs -- II [PDF]
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, we
Lau, Gee-Choon, Shiu, Wai Chee
core +1 more source
Local Total Antimagic Chromatic Number for the Disjoint Union of Star Graphs
Let $G$ be a graph with $n$ vertices and $m$ edges without isolated vertices.A local total antimagic labeling of a graph $G$ is defined as there is a bijection $f:V(G)\cup E(G)\rightarrow \{ 1,2,...,n+m\}$, with for any two adjacent vertices $u$ and $v$
Moviri Chettiar Nalliah +1 more
core +1 more source
The Local Antimagic On Disjoint Union of Some Family Graphs [PDF]
, 2019 A graph in this paper is nontrivial, finite, connected, simple, and undirected. Graph consists of a vertex set and edge set. Let u,v be two elements in vertex set, and q is the cardinality of edge set in G, a bijective function from the edge ...
Marsidi, Marsidi, Agustin, Ika Hesti
core +1 more source
A note on local antimagic chromatic number of lexicographic product graphs
, 2022 Let $G = (V,E)$ be a connected simple graph. A bijection $f: E \rightarrow \{1,2,\ldots,|E|\}$ is called a local antimagic labeling of $G$ if $f^+(u) \neq f^+(v)$ holds for any two adjacent vertices $u$ and $v$, where $f^+(u) = \sum_{e\in E(u)} f(e)$ and
Nalliah, M. +4 more
core