DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

Article in press


Authors:

G.C. Lau, H.-K. Ng, W.C. Shiu

Title:

On local antimagic chromatic number of cycle-related join graphs

Source:

Discussiones Mathematicae Graph Theory

Received: 2018-05-21, Revised: 2018-08-27, Accepted: 2018-08-27, https://doi.org/10.7151/dmgt.2177

Abstract:

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 $f^+(x)= \sum f(e)$, with $e$ ranging over all the edges incident to $x$. The local antimagic chromatic number of $G$, denoted by $\chi_{la}(G)$, is the minimum number of distinct induced vertex labels over all local antimagic labelings of $G$. In this paper, several sufficient conditions for $\chi_{la}(H)\le \chi_{la}(G)$ are obtained, where $H$ is obtained from $G$ with a certain edge deleted or added. We then determined the exact value of the local antimagic chromatic number of many cycle-related join graphs.

Keywords:

local antimagic labeling, local antimagic chromatic number, cycle, join graphs

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