NDLI: Distance Antimagic Product Graphs

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Distance Antimagic Product Graphs

Content Provider	MDPI
Author	Simanjuntak, Rinovia Tritama, Aholiab
Copyright Year	2022
Abstract	A distance antimagic graph is a graph G admitting a bijection $f : V (G) \to {1, 2, \dots, \| V (G) \|}$ such that for two distinct vertices x and y, $ω (x) \neq ω (y)$ , where $ω (x) = \sum_{y \in N (x)} f (y)$ , for $N (x)$ the open neighborhood of x. It was conjectured that a graph G is distance antimagic if and only if G contains no two vertices with the same open neighborhood. In this paper, we study several distance antimagic product graphs. The products under consideration are the three fundamental graph products (Cartesian, strong, direct), the lexicographic product, and the corona product. We investigate the consequence of the non-commutative (or sometimes called non-symmetric) property of the last two products to the antimagicness of the product graphs.
Starting Page	1411
e-ISSN	20738994
DOI	10.3390/sym14071411
Journal	Symmetry
Issue Number	7
Volume Number	14
Language	English
Publisher	MDPI
Publisher Date	2022-07-09
Access Restriction	Open
Subject Keyword	Symmetry Hardware and Architecturee Logic Distance Antimagic Labeling Graph Product Cartesian Product Strong Product Direct Product Lexicographic Product Corona Product
Content Type	Text
Resource Type	Article

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