Volume 4, Issue 4, December 2019, Page: 45-50
Signed Product Cordial of the Sum and Union of Two Fourth Power of Paths and Cycles
Shokry Nada, Department of Mathematics, Faculty of Science, Menoyfia University, Cairo, Egypt
Amani Elrayes, Institute of National Planning, Cairo, Egypt
Ashraf Elrokh, Department of Mathematics, Faculty of Science, Menoyfia University, Cairo, Egypt
Aya Rabie, Institute of National Planning, Cairo, Egypt
Received: Jun. 15, 2019;       Accepted: Aug. 12, 2019;       Published: Dec. 30, 2019
DOI: 10.11648/j.mlr.20190404.11      View  37      Downloads  11
Abstract
A simple graph is said to be signed product cordial if it admits ±1 labeling that satisfies certain conditions. Our aim in this paper is to contribute some new results on signed product cordial labeling and present necessary and sufficient conditions for signed product cordial of the sum and union of two fourth power of paths. We also study the signed product cordiality of the sum and union of fourth power cycles The residue classes modulo 4 are accustomed to find suitable labelings for each class to achieve our task. We have shown that the union and the join of any two fourth power of paths are always signed product cordial. Howover, the join and union of fourth power of cycles are only signed codial with some expectional situations.
Keywords
Fourth Power, Sum Graph, Union Graph, Signed Product Cordial Graph, AMS Classification: 05C78, 05C75, 05C20
To cite this article
Shokry Nada, Amani Elrayes, Ashraf Elrokh, Aya Rabie, Signed Product Cordial of the Sum and Union of Two Fourth Power of Paths and Cycles, Machine Learning Research. Vol. 4, No. 4, 2019, pp. 45-50. doi: 10.11648/j.mlr.20190404.11
Copyright
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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