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Edge Even Graceful Labeling of Polar Grid Graphs

1
Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah 41411, Saudi Arabia
2
Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El Kom 32511, Egypt
Symmetry 2019, 11(1), 38; https://doi.org/10.3390/sym11010038
Received: 6 December 2018 / Revised: 20 December 2018 / Accepted: 23 December 2018 / Published: 2 January 2019
(This article belongs to the Special Issue Discrete Mathematics and Symmetry)
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Abstract

Edge Even Graceful Labelingwas first defined byElsonbaty and Daoud in 2017. An edge even graceful labeling of a simple graph G with p vertices and q edges is a bijection f from the edges of the graph to the set { 2 , 4 , , 2 q } such that, when each vertex is assigned the sum of all edges incident to it mod 2 r where r = max { p , q } , the resulting vertex labels are distinct. In this paper we proved necessary and sufficient conditions for the polar grid graph to be edge even graceful graph. View Full-Text
Keywords: graceful labeling; edge graceful labeling; edge even graceful labeling; polar grid graph graceful labeling; edge graceful labeling; edge even graceful labeling; polar grid graph
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Daoud, S.N. Edge Even Graceful Labeling of Polar Grid Graphs. Symmetry 2019, 11, 38.

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