The Cordial Labeling for the Four-Leaved Rose Graph

Ashraf Elrokh

doi:doi:10.11648/j.acm.20180704.14

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The Cordial Labeling for the Four-Leaved Rose Graph

Ashraf Elrokh

Published in Applied and Computational Mathematics (Volume 7, Issue 4)

Received: 22 June 2018 Accepted: 31 August 2018 Published: 15 October 2018

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Abstract

A cactus graph with four blocks which are all cycles, not necessarily be of the same size, is called four-leaved rose graph and denoted by L_{n, m, k, s}, where n, m, k and s represent she sizes of the four cycles. A cordial graph is a graph whose vertices and edges have 0-1 labeling in such a way that the number of vertices (edges) labelled with zeros and the number of vertices (edges) labelled with ones differ absolutely by at most one .In this paper, we study this graph in detail and show that any four-leaved rose graph is cordial for all n, m, k and s except possibly at n, m are odd with (k + s) = 0(mod4) or n, m are even with (k + s) = 2(mod4). Our technique depends on the methods that partition off the set of positive integers and then use suitable labeling in each division of the partition to achieve our results. AMS classification 05C76, 05C78

Published in	Applied and Computational Mathematics (Volume 7, Issue 4)
DOI	10.11648/j.acm.20180704.14
Page(s)	203-211
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), 2018. Published by Science Publishing Group

Keywords

Cactus Graph, Cordial Labeling, Four-Leaved Rose Graph

References

[1]	Rosa, A. , On certain valuations of the vertices of a graph, Theory of Graphs( Internat Symposium, Rome, July 1966),Gordon and Breach, N.Y.and Dunod Paris, (1967) 349- 355.
[2]	Graham, R. L. and Sloane, N.J.A., On additive bases and harmonious graphs, SIAM J. Alg. Discrete Math. 1, (1980) 382-404.
[3]	Elrokh, A. and Atef Mohamed, The cordiality of lemniscate graph and its second power, Malaysian journal of mathematical science , 2017 under review
[4]	Elrokh, A., The cordiality of the three-leaved rose graph, submitted 2018.
[5]	Diab, A. T. , On Cordial Labelings of Wheels with Other Graphs, ARS Combinatoria 100, (2011) 265-279.
[6]	Golomb, S. W., How to number a graph in Graph Theory and Computing,R.C. Read, ed., Academic Press, New York, (1972) 23-37.
[7]	Gallian, J. A. , A dynamic survey of graph labeling, The Electronic Journal of Combina- torics 17, December 29 (2014).
[8]	Cahit, I. , Cordial Graphs: A Weaker Version of Graceful and Harmonious Graphs, Ars Combin. 23(1987) 201-207.
[9]	Kirchherr, W. W., On the cordiality of some specific graphs, ARS Combinatoria 31(1991), pp 127-138.
[10]	Lee, S. M. and Liu, A. , A construction of cordial graphs from smaller cordial graphs, Ars Combin., 32(1991) 209-214.

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APA Style

Ashraf Elrokh. (2018). The Cordial Labeling for the Four-Leaved Rose Graph. Applied and Computational Mathematics, 7(4), 203-211. https://doi.org/10.11648/j.acm.20180704.14

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ACS Style

Ashraf Elrokh. The Cordial Labeling for the Four-Leaved Rose Graph. Appl. Comput. Math. 2018, 7(4), 203-211. doi: 10.11648/j.acm.20180704.14

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AMA Style

Ashraf Elrokh. The Cordial Labeling for the Four-Leaved Rose Graph. Appl Comput Math. 2018;7(4):203-211. doi: 10.11648/j.acm.20180704.14

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@article{10.11648/j.acm.20180704.14,
  author = {Ashraf Elrokh},
  title = {The Cordial Labeling for the Four-Leaved Rose Graph},
  journal = {Applied and Computational Mathematics},
  volume = {7},
  number = {4},
  pages = {203-211},
  doi = {10.11648/j.acm.20180704.14},
  url = {https://doi.org/10.11648/j.acm.20180704.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20180704.14},
  abstract = {A cactus graph with four blocks which are all cycles, not necessarily be of the same size, is called four-leaved rose graph and denoted by Ln, m, k, s, where n, m, k and s represent she sizes of the four cycles. A cordial graph is a graph whose vertices and edges have 0-1 labeling in such a way that the number of vertices (edges) labelled with zeros and the number of vertices (edges) labelled with ones differ absolutely by at most one .In this paper, we study this graph in detail and show that any four-leaved rose graph is cordial for all n, m, k and s except possibly at n, m are odd with (k + s) = 0(mod4) or n, m are even with (k + s) = 2(mod4). Our technique depends on the methods that partition off the set of positive integers and then use suitable labeling in each division of the partition to achieve our results. AMS classification 05C76, 05C78},
 year = {2018}
}

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TY  - JOUR
T1  - The Cordial Labeling for the Four-Leaved Rose Graph
AU  - Ashraf Elrokh
Y1  - 2018/10/15
PY  - 2018
N1  - https://doi.org/10.11648/j.acm.20180704.14
DO  - 10.11648/j.acm.20180704.14
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 203
EP  - 211
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20180704.14
AB  - A cactus graph with four blocks which are all cycles, not necessarily be of the same size, is called four-leaved rose graph and denoted by Ln, m, k, s, where n, m, k and s represent she sizes of the four cycles. A cordial graph is a graph whose vertices and edges have 0-1 labeling in such a way that the number of vertices (edges) labelled with zeros and the number of vertices (edges) labelled with ones differ absolutely by at most one .In this paper, we study this graph in detail and show that any four-leaved rose graph is cordial for all n, m, k and s except possibly at n, m are odd with (k + s) = 0(mod4) or n, m are even with (k + s) = 2(mod4). Our technique depends on the methods that partition off the set of positive integers and then use suitable labeling in each division of the partition to achieve our results. AMS classification 05C76, 05C78
VL  - 7
IS  - 4
ER  -

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Author Information

Ashraf Elrokh

Department of Math, Faculty of Science, Menoufia University, Shebeen Elkom, Egypt

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APA Style

Ashraf Elrokh. (2018). The Cordial Labeling for the Four-Leaved Rose Graph. Applied and Computational Mathematics, 7(4), 203-211. https://doi.org/10.11648/j.acm.20180704.14

Copy | Download

ACS Style

Ashraf Elrokh. The Cordial Labeling for the Four-Leaved Rose Graph. Appl. Comput. Math. 2018, 7(4), 203-211. doi: 10.11648/j.acm.20180704.14

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AMA Style

Ashraf Elrokh. The Cordial Labeling for the Four-Leaved Rose Graph. Appl Comput Math. 2018;7(4):203-211. doi: 10.11648/j.acm.20180704.14

Copy | Download

@article{10.11648/j.acm.20180704.14,
  author = {Ashraf Elrokh},
  title = {The Cordial Labeling for the Four-Leaved Rose Graph},
  journal = {Applied and Computational Mathematics},
  volume = {7},
  number = {4},
  pages = {203-211},
  doi = {10.11648/j.acm.20180704.14},
  url = {https://doi.org/10.11648/j.acm.20180704.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20180704.14},
  abstract = {A cactus graph with four blocks which are all cycles, not necessarily be of the same size, is called four-leaved rose graph and denoted by Ln, m, k, s, where n, m, k and s represent she sizes of the four cycles. A cordial graph is a graph whose vertices and edges have 0-1 labeling in such a way that the number of vertices (edges) labelled with zeros and the number of vertices (edges) labelled with ones differ absolutely by at most one .In this paper, we study this graph in detail and show that any four-leaved rose graph is cordial for all n, m, k and s except possibly at n, m are odd with (k + s) = 0(mod4) or n, m are even with (k + s) = 2(mod4). Our technique depends on the methods that partition off the set of positive integers and then use suitable labeling in each division of the partition to achieve our results. AMS classification 05C76, 05C78},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - The Cordial Labeling for the Four-Leaved Rose Graph
AU  - Ashraf Elrokh
Y1  - 2018/10/15
PY  - 2018
N1  - https://doi.org/10.11648/j.acm.20180704.14
DO  - 10.11648/j.acm.20180704.14
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 203
EP  - 211
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20180704.14
AB  - A cactus graph with four blocks which are all cycles, not necessarily be of the same size, is called four-leaved rose graph and denoted by Ln, m, k, s, where n, m, k and s represent she sizes of the four cycles. A cordial graph is a graph whose vertices and edges have 0-1 labeling in such a way that the number of vertices (edges) labelled with zeros and the number of vertices (edges) labelled with ones differ absolutely by at most one .In this paper, we study this graph in detail and show that any four-leaved rose graph is cordial for all n, m, k and s except possibly at n, m are odd with (k + s) = 0(mod4) or n, m are even with (k + s) = 2(mod4). Our technique depends on the methods that partition off the set of positive integers and then use suitable labeling in each division of the partition to achieve our results. AMS classification 05C76, 05C78
VL  - 7
IS  - 4
ER  -

Copy | Download