G. Lau

Complete characterization of disconnected one-point unions of cycles with local antimagic chromatic number 2

Gee-Choon Lau, Wai Chee Shiu

A graph $G = (V, E)$ that admits a bijective edge labeling $f : E \to {1, \dots, ∣ E ∣}$ is local antimagic if $f$ induces a vertex labeling $f^{+}$ such that for any pair of adjacent v…

Local Antimagic Chromatic Number of Middle Graph and Direct Product of Graphs

Huimin Xu, Gee-Choon Lau, Ruixue Zhang

An edge labeling of a connected graph $G = (V, E)$ is called a local antimagic labeling if it is a bijection $f : E \to {1, 2, \dots, ∣ E ∣}$ such that for any…

Necessary and sufficient conditions of a class of bipartite graphs with local antimagic chromatic number 2 - an algebraic approach

Gee-Choon Lau, Wai Chee Shiu

For a connected graph $G = (V, E)$ , a bijective edge labeling $f : E \to {1, \dots, ∣ E ∣}$ is a local antimagic labeling of $G$ if it induces a vertex labeling $f^{+}$ such that for an…

A novel approach to determining chromatic number induced by labelings

Gee-Choon Lau, Wai Chee Shiu, Zhen Bin Gao

Given a simple graph $G = (V, E)$ of order $p$ and size $q$ , a bijection $f : V \cup E \to {1, 2, \dots, p + q}$ is a local total neighborhood antimagic labeling of $G$ if the induced…

On local antimagic chromatic number of the join of two special families of graphs -- II

Gee-Choon Lau, Wai Chee Shiu

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 an…

New Families of tripartite graphs with local antimagic chromatic number 3

Gee-Choon Lau, Wai Chee Shiu

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 $f^{+} : V (G) \to N$ such that $f^+(u) \ne f^…

On local antimagic chromatic numbers of the join of two special families of graphs

Gee-Choon Lau, Wai Chee Shiu

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)…

On local antimagic total chromatic number of certain one point union of graphs

Gee-Choon Lau

Let $G = (V, E)$ be a connected simple graph of order $p$ and size $q$ . A bijection $f : V (G) \cup E (G) \to {1, 2, \dots, p + q}$ is called a local antimagic total labeling of $G$ if for…

Construction of local antimagic 3-colorable graphs of fixed even size -- matrix approach

Gee-Choon Lau, Wai Chee Shiu, M. Nalliah +1

An edge labeling of a connected graph $G = (V, E)$ is said to be local antimagic if it is a bijection $f : E \to {1, \dots, ∣ E ∣}$ such that for any pair of adjacent vertices $x$ and…

Constructions of local antimagic 3-colorable graphs of fixed odd size | matrix approach

Gee-Choon Lau, Wai Chee Shiu, K. Premalatha +1

An edge labeling of a connected graph $G = (V, E)$ is said to be local antimagic if there is a bijection $f : E \to {1, \dots, ∣ E ∣}$ such that for any pair of adjacent vertices $x$ …

Complete characterization of graphs with local total antimagic chromatic number 3

G. C. Lau

A total labeling of a graph $G = (V, E)$ is said to be local total antimagic if it is a bijection $f : V \cup E \to {1, \dots, ∣ V ∣ + ∣ E ∣}$ such that adjacent vertices, adjacent edges,…

math.CO2023

An algorithmic approach in constructing infinitely many even size graphs with local antimagic chromatic number 3

Gee-Choon Lau

An edge labeling of a connected graph $G = (V, E)$ is said to be local antimagic if it is a bijection $f : E \to {1, \dots, ∣ E ∣}$ such that for any pair of adjacent vertices $x$ and…

math.CO2023

On bridge graphs with local antimagic chromatic number 3

W. C. Shiu, G. C. Lau, R. X. Zhang

Let $G = (V, E)$ be a connected graph. A bijection $f : E \to {1, \dots, ∣ E ∣}$ is called a local antimagic labeling if for any two adjacent vertices $x$ and $y$ , $f^{+} (x) \neq = f^{+} (y)$ …

math.CO2022★ 2 cited

Complete characterization of s-bridge graphs with local antimagic chromatic number 2

Gee-Choon Lau, Wai-Chee Shiu, Ruixue Zhang +2

An edge labeling of a connected graph $G = (V, E)$ is said to be local antimagic if it is a bijection $f : E \to {1, \dots, ∣ E ∣}$ such that for any pair of adjacent vertices $x$ and…

A note on local antimagic chromatic number of lexicographic product graphs

Gee-Choon Lau, Wai-Chee Shiu, K. Premalatha +2

Let $G = (V, E)$ be a connected simple graph. A bijection $f : E \to {1, 2, \dots, ∣ E ∣}$ is called a local antimagic labeling of $G$ if $f^{+} (u) \neq = f^{+} (v)$ holds for any two…

Sudoku Number of Graphs

Gee-Choon Lau, J. Maria Jeyaseeli, Wai-Chee Shiu +1

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 $χ (G) = k$ and let $S \subseteq V .$ Le…

On local antimagic chromatic number of lexicographic product graphs

Gee-Choon Lau, Wai-Chee Shiu

Let $G = (V, E)$ be a connected simple graph of order $p$ and size $q$ . A graph $G$ is called local antimagic if $G$ admits a local antimagic labeling. A bijection $f : E \to \{1,2,…

On local antimagic chromatic number of a corona product graph

Gee-Choon Lau, M. Nalliah

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 respective…