Signed Product Cordial of the Sum and Union of Two Fourth Power of Paths and Cycles

Shokry Nada; Amani Elrayes; Ashraf Elrokh; Aya Rabie

doi:doi:10.11648/j.mlr.20190404.11

| Peer-Reviewed

Signed Product Cordial of the Sum and Union of Two Fourth Power of Paths and Cycles

Shokry Nada, Amani Elrayes, Ashraf Elrokh, Aya Rabie

Published in Machine Learning Research (Volume 4, Issue 4)

Received: 15 June 2019 Accepted: 12 August 2019 Published: 30 December 2019

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

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.

Published in	Machine Learning Research (Volume 4, Issue 4)
DOI	10.11648/j.mlr.20190404.11
Page(s)	45-50
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2019. Published by Science Publishing Group

Keywords

Fourth Power, Sum Graph, Union Graph, Signed Product Cordial Graph, AMS Classification: 05C78, 05C75, 05C20

References

[1]	A. Balaban, "Application of Graph Theory in Chemistry", Journal of Chemical Information and Computer Science, 334-343 (2019).
[2]	I. Cahit, Cordial Graphs. A weaker version of graceful and harmonious Graphs, Ars Combinatoria, 23: 201-207 (1987).
[3]	A. Chakraborty, T. Dutta, S. Mondal, and A. Nath, "Application of Graph Theory in Social Media", International Journal of Computer Sciences and Engineering, vol. -6, 722-729 (2018).
[4]	J. Devaraj and P. Delphy. On signed cordial graph, Int. J. of Mathematical Sciences and Applications, Vol. 1, No. 3, September 1156-1167 (2011).
[5]	A. T. Diab, Study of some problems of cordial graphs, Ars Combin, 92, 255-261 (2009).
[6]	A. T. Diab, Generalization of some results on cordial graphs, Ars Combin, 99, 161-173 (2011).
[7]	F. Farahani, W. Karwski, and N. R. Lighthall, "Application of Graph Theory for Identifing Connectivity Patterns in Human Brain Network: A S ystematic Review", frontiers in Neuroscience, (2019).
[8]	J. A. Gallian, A Dynamic Survey of Graph Labeling, The Electronic Journal of Combinatorics, DS6, (2014).
[9]	A. Rosa, On certain valuations of the vertices of a graph, Theory of graphs (Internat. Symposium, Rome, July 1996), Gordon and Breach, N. Y. and Dunod Paris 349- 355, (1967).
[10]	P. Sumathi, A. Mahalakshmi, "Quotient-3 Cordial Labeling for Path Related Graphs", Applied Mathematics and Scientific Computing, 555-561 (2019).
[11]	M. Sundaram, R. Ponraj, and S. Somasundaram, Product cordial labeling of graph, Bulletin of Pure and Applied Science, vol. 23, 155-163, (2004).
[12]	R. Ponraj, K. Annathurai and R. Kala, "Remainder Cordiality of some Graphs", Palestine Journal of Mathematics, Vol. 8 (1), 367-372 (2019).

Cite This Article

Plain Text BibTeX RIS

APA Style

Shokry Nada, Amani Elrayes, Ashraf Elrokh, Aya Rabie. (2019). Signed Product Cordial of the Sum and Union of Two Fourth Power of Paths and Cycles. Machine Learning Research, 4(4), 45-50. https://doi.org/10.11648/j.mlr.20190404.11

Copy | Download

ACS Style

Shokry Nada; Amani Elrayes; Ashraf Elrokh; Aya Rabie. Signed Product Cordial of the Sum and Union of Two Fourth Power of Paths and Cycles. Mach. Learn. Res. 2019, 4(4), 45-50. doi: 10.11648/j.mlr.20190404.11

Copy | Download

AMA Style

Shokry Nada, Amani Elrayes, Ashraf Elrokh, Aya Rabie. Signed Product Cordial of the Sum and Union of Two Fourth Power of Paths and Cycles. Mach Learn Res. 2019;4(4):45-50. doi: 10.11648/j.mlr.20190404.11

Copy | Download

@article{10.11648/j.mlr.20190404.11,
  author = {Shokry Nada and Amani Elrayes and Ashraf Elrokh and Aya Rabie},
  title = {Signed Product Cordial of the Sum and Union of Two Fourth Power of Paths and Cycles},
  journal = {Machine Learning Research},
  volume = {4},
  number = {4},
  pages = {45-50},
  doi = {10.11648/j.mlr.20190404.11},
  url = {https://doi.org/10.11648/j.mlr.20190404.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mlr.20190404.11},
  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.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Signed Product Cordial of the Sum and Union of Two Fourth Power of Paths and Cycles
AU  - Shokry Nada
AU  - Amani Elrayes
AU  - Ashraf Elrokh
AU  - Aya Rabie
Y1  - 2019/12/30
PY  - 2019
N1  - https://doi.org/10.11648/j.mlr.20190404.11
DO  - 10.11648/j.mlr.20190404.11
T2  - Machine Learning Research
JF  - Machine Learning Research
JO  - Machine Learning Research
SP  - 45
EP  - 50
PB  - Science Publishing Group
SN  - 2637-5680
UR  - https://doi.org/10.11648/j.mlr.20190404.11
AB  - 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.
VL  - 4
IS  - 4
ER  -

Copy | Download

Author Information

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

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Shokry Nada, Amani Elrayes, Ashraf Elrokh, Aya Rabie. (2019). Signed Product Cordial of the Sum and Union of Two Fourth Power of Paths and Cycles. Machine Learning Research, 4(4), 45-50. https://doi.org/10.11648/j.mlr.20190404.11

Copy | Download

ACS Style

Shokry Nada; Amani Elrayes; Ashraf Elrokh; Aya Rabie. Signed Product Cordial of the Sum and Union of Two Fourth Power of Paths and Cycles. Mach. Learn. Res. 2019, 4(4), 45-50. doi: 10.11648/j.mlr.20190404.11

Copy | Download

AMA Style

Shokry Nada, Amani Elrayes, Ashraf Elrokh, Aya Rabie. Signed Product Cordial of the Sum and Union of Two Fourth Power of Paths and Cycles. Mach Learn Res. 2019;4(4):45-50. doi: 10.11648/j.mlr.20190404.11

Copy | Download

@article{10.11648/j.mlr.20190404.11,
  author = {Shokry Nada and Amani Elrayes and Ashraf Elrokh and Aya Rabie},
  title = {Signed Product Cordial of the Sum and Union of Two Fourth Power of Paths and Cycles},
  journal = {Machine Learning Research},
  volume = {4},
  number = {4},
  pages = {45-50},
  doi = {10.11648/j.mlr.20190404.11},
  url = {https://doi.org/10.11648/j.mlr.20190404.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mlr.20190404.11},
  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.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Signed Product Cordial of the Sum and Union of Two Fourth Power of Paths and Cycles
AU  - Shokry Nada
AU  - Amani Elrayes
AU  - Ashraf Elrokh
AU  - Aya Rabie
Y1  - 2019/12/30
PY  - 2019
N1  - https://doi.org/10.11648/j.mlr.20190404.11
DO  - 10.11648/j.mlr.20190404.11
T2  - Machine Learning Research
JF  - Machine Learning Research
JO  - Machine Learning Research
SP  - 45
EP  - 50
PB  - Science Publishing Group
SN  - 2637-5680
UR  - https://doi.org/10.11648/j.mlr.20190404.11
AB  - 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.
VL  - 4
IS  - 4
ER  -

Copy | Download