The Cordiality of the Join and Union of the Second Power of Fans

Shokry Nada; Ashraf Elrokh; Eman Elshafey

doi:doi:10.11648/j.acm.20180706.11

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The Cordiality of the Join and Union of the Second Power of Fans

Shokry Nada, Ashraf Elrokh, Eman Elshafey

Published in Applied and Computational Mathematics (Volume 7, Issue 6)

Received: 9 December 2018 Accepted: 5 January 2019 Published: 28 January 2019

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Abstract

A graph is called cordial if it has a 0-1 labeling that satisfies certain conditions. A second power of a fan F_n ² is the join of the null graph N₁ and the second power of path P_n², i.e. F_n² = N₁ + P_n². In this paper, we study the cordiality of the join and union of pairs of the second power of fans. and give the necessary and sufficient conditions that the join of two second powers of fans is cordial. we extend these results to investigate the cordiality of the join and the union of pairs of the second power of fans. Similar study is given for the union of such second power of fans. AMS Classification: 05C78.

Published in	Applied and Computational Mathematics (Volume 7, Issue 6)
DOI	10.11648/j.acm.20180706.11
Page(s)	219-224
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

Join Graph, Second Power Graph, Cordial Graph

References

[1]	Cahit, On cordial and 3-equitable labelings of graphs, Utilities Math., 37 (1990).
[2]	A. T. Diab, and E. A. Elsakhaw,. Some Results on Cordial Graphs, Proc. Math. Phys. Soc. Egypt, No.7, pp. 67-87 (2002).
[3]	A. T. Diab,Study of Some Problems of Cordial Graphs, Ars Combinatoria 92 (2009), pp. 255-261.
[4]	A. T. Diab, On Cordial Labelings of the Second Power of Paths with Other Graphs, Ars Combinatoria 97A(2010), pp. 327-343.
[5]	J. A.Gallian, A dynamic survey of graph labeling, The Electronic Journal of Combinatorics, (December 29, 2014).
[6]	S. W. Golomb, How to number a graph in Graph Theory and Computing, R.C. Read, ed., Academic Press, New York (1972) 23-37.
[7]	R. L. Graham and N. J. A.Sloane, On additive bases and harmonious graphs, SIAM J. Alg. Discrete Math.,1(1980) 382404.
[8]	Rosa, On certain valuations of the vertices of a graph, Theory of Graphs (Internet. Symposium, Rome, July 1966), Gordon and Breach, N. Y. and Dunod Paris (1967) 349-355.

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APA Style

Shokry Nada, Ashraf Elrokh, Eman Elshafey. (2019). The Cordiality of the Join and Union of the Second Power of Fans. Applied and Computational Mathematics, 7(6), 219-224. https://doi.org/10.11648/j.acm.20180706.11

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ACS Style

Shokry Nada; Ashraf Elrokh; Eman Elshafey. The Cordiality of the Join and Union of the Second Power of Fans. Appl. Comput. Math. 2019, 7(6), 219-224. doi: 10.11648/j.acm.20180706.11

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AMA Style

Shokry Nada, Ashraf Elrokh, Eman Elshafey. The Cordiality of the Join and Union of the Second Power of Fans. Appl Comput Math. 2019;7(6):219-224. doi: 10.11648/j.acm.20180706.11

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@article{10.11648/j.acm.20180706.11,
  author = {Shokry Nada and Ashraf Elrokh and Eman Elshafey},
  title = {The Cordiality of the Join and Union of the Second Power of Fans},
  journal = {Applied and Computational Mathematics},
  volume = {7},
  number = {6},
  pages = {219-224},
  doi = {10.11648/j.acm.20180706.11},
  url = {https://doi.org/10.11648/j.acm.20180706.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20180706.11},
  abstract = {A graph is called cordial if it has a 0-1 labeling that satisfies certain conditions. A second power of a fan Fn 2 is the join of the null graph N1 and the second power of path Pn2, i.e. Fn2 = N1 + Pn2. In this paper, we study the cordiality of the join and union of pairs of the second power of fans. and give the necessary and sufficient conditions that the join of two second powers of fans is cordial. we extend these results to investigate the cordiality of the join and the union of pairs of the second power of fans. Similar study is given for the union of such second power of fans. AMS Classification: 05C78.},
 year = {2019}
}

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TY  - JOUR
T1  - The Cordiality of the Join and Union of the Second Power of Fans
AU  - Shokry Nada
AU  - Ashraf Elrokh
AU  - Eman Elshafey
Y1  - 2019/01/28
PY  - 2019
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DO  - 10.11648/j.acm.20180706.11
T2  - Applied and Computational Mathematics
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AB  - A graph is called cordial if it has a 0-1 labeling that satisfies certain conditions. A second power of a fan Fn 2 is the join of the null graph N1 and the second power of path Pn2, i.e. Fn2 = N1 + Pn2. In this paper, we study the cordiality of the join and union of pairs of the second power of fans. and give the necessary and sufficient conditions that the join of two second powers of fans is cordial. we extend these results to investigate the cordiality of the join and the union of pairs of the second power of fans. Similar study is given for the union of such second power of fans. AMS Classification: 05C78.
VL  - 7
IS  - 6
ER  -

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Author Information

Shokry Nada

Department of Math, Faculty of Science, Menoyfia University, Shebeen Elkom, Egypt
Ashraf Elrokh

Department of Math, Faculty of Science, Menoyfia University, Shebeen Elkom, Egypt
Eman Elshafey

Department of Math, Faculty of Science, El- Azhar University, Cairo, Egypt

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APA Style

Shokry Nada, Ashraf Elrokh, Eman Elshafey. (2019). The Cordiality of the Join and Union of the Second Power of Fans. Applied and Computational Mathematics, 7(6), 219-224. https://doi.org/10.11648/j.acm.20180706.11

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ACS Style

Shokry Nada; Ashraf Elrokh; Eman Elshafey. The Cordiality of the Join and Union of the Second Power of Fans. Appl. Comput. Math. 2019, 7(6), 219-224. doi: 10.11648/j.acm.20180706.11

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AMA Style

Shokry Nada, Ashraf Elrokh, Eman Elshafey. The Cordiality of the Join and Union of the Second Power of Fans. Appl Comput Math. 2019;7(6):219-224. doi: 10.11648/j.acm.20180706.11

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@article{10.11648/j.acm.20180706.11,
  author = {Shokry Nada and Ashraf Elrokh and Eman Elshafey},
  title = {The Cordiality of the Join and Union of the Second Power of Fans},
  journal = {Applied and Computational Mathematics},
  volume = {7},
  number = {6},
  pages = {219-224},
  doi = {10.11648/j.acm.20180706.11},
  url = {https://doi.org/10.11648/j.acm.20180706.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20180706.11},
  abstract = {A graph is called cordial if it has a 0-1 labeling that satisfies certain conditions. A second power of a fan Fn 2 is the join of the null graph N1 and the second power of path Pn2, i.e. Fn2 = N1 + Pn2. In this paper, we study the cordiality of the join and union of pairs of the second power of fans. and give the necessary and sufficient conditions that the join of two second powers of fans is cordial. we extend these results to investigate the cordiality of the join and the union of pairs of the second power of fans. Similar study is given for the union of such second power of fans. AMS Classification: 05C78.},
 year = {2019}
}

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TY  - JOUR
T1  - The Cordiality of the Join and Union of the Second Power of Fans
AU  - Shokry Nada
AU  - Ashraf Elrokh
AU  - Eman Elshafey
Y1  - 2019/01/28
PY  - 2019
N1  - https://doi.org/10.11648/j.acm.20180706.11
DO  - 10.11648/j.acm.20180706.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 219
EP  - 224
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20180706.11
AB  - A graph is called cordial if it has a 0-1 labeling that satisfies certain conditions. A second power of a fan Fn 2 is the join of the null graph N1 and the second power of path Pn2, i.e. Fn2 = N1 + Pn2. In this paper, we study the cordiality of the join and union of pairs of the second power of fans. and give the necessary and sufficient conditions that the join of two second powers of fans is cordial. we extend these results to investigate the cordiality of the join and the union of pairs of the second power of fans. Similar study is given for the union of such second power of fans. AMS Classification: 05C78.
VL  - 7
IS  - 6
ER  -

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