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Edge Even Graceful Labeling of Cylinder Grid Graph

1
Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah 41411, Saudi Arabia
2
Department of Mathematics, Faculty of Science, Ain Shams University, Cairo 11566, Egypt
3
Department of Mathematics and Compuer Science, Faculty of Science, Menoufia University, Shebin El Kom 32511, Egypt
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(4), 584; https://doi.org/10.3390/sym11040584
Received: 26 March 2019 / Revised: 12 April 2019 / Accepted: 14 April 2019 / Published: 22 April 2019
(This article belongs to the Special Issue Discrete Mathematics and Symmetry)
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Abstract

Edge even graceful labeling (e.e.g., l.) of graphs is a modular technique of edge labeling of graphs, introduced in 2017. An e.e.g., l. of simple finite undirected graph G = ( V ( G ) , E ( G ) ) of order P = | ( V ( G ) | and size q = | E ( G ) | is a bijection f : E ( G ) { 2 , 4 , , 2 q } , such that when each vertex v V ( G ) is assigned the modular sum of the labels (images of f ) of the edges incident to v , the resulting vertex labels are distinct mod 2 r , where r = max ( p , q ) . In this work, the family of cylinder grid graphs are studied. Explicit formulas of e.e.g., l. for all of the cases of each member of this family have been proven. View Full-Text
Keywords: graceful labeling; edge even graceful labeling; cylinder grid graph graceful labeling; edge even graceful labeling; cylinder grid graph
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Elsonbaty, A.A.; Daoud, S.N. Edge Even Graceful Labeling of Cylinder Grid Graph. Symmetry 2019, 11, 584.

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