Enumeration of Triangles in Cayley Graphs

Levaku Madhavi; Tekuri Chalapathi

doi:doi:10.11648/j.pamj.20150403.21

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Enumeration of Triangles in Cayley Graphs

Levaku Madhavi, Tekuri Chalapathi

Published in Pure and Applied Mathematics Journal (Volume 4, Issue 3)

Received: 12 May 2015 Accepted: 23 May 2015 Published: 11 June 2015

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Abstract

Significant contributions can be found on the study of the cycle structure in graphs, particularly in Cayley graphs. Determination of Hamilton cycles and triangles, the longest and shortest cycles attracts special attention. In this paper an enumeration process for the determination of number of triangles in the Cayley graph associated with a group not necessarily abelian and a symmetric subset of the group.

Published in	Pure and Applied Mathematics Journal (Volume 4, Issue 3)
DOI	10.11648/j.pamj.20150403.21
Page(s)	128-132
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), 2015. Published by Science Publishing Group

Keywords

Cayley Graphs, Fundamental Triangle, Triangle and Group

References

[1]	G. Andrews, Number Theory, Dover publications Inc.,1971.
[2]	P. Berrizbeitia and R. E. Giudici, Counting Pure k-cycles in Sequences of Cayley graphs, Discrete Maths. 149 (1996), 11-18.
[3]	P. Berrizbeitia, and R. E. Giudici, On cycles in the Sequence of Unitary Cayley graphs, Reporte Técnico No.01-95, Universidad Simon Bolivar, Dpto.de Matahematicas, Caracas, Venezula (1995).
[4]	T. Chalapati, L. Madhavi and S. Venkata Ramana, Enumeration of Triangles in a Divisor Cayley graph, MEJS 1 (2013), 163-173.
[5]	I. Dejter and R. E. Giudici, On Unitary Cayley graphs, JCMCC 18 (1995), 121 – 124.
[6]	E. Dickson, History of Theory of Numbers, Vol.1, Chelsea Publishing Company, 1952.
[7]	B. Maheswari and L. Madhavi, Enumeration of Triangles and Hamilton Cycles in Quadratic Residue Cayley graphs, Chamchuri Journal of Mathematics 1 (2009), 95-103.
[8]	B. Maheswari and L. Madhavi, Enumeration of Hamilton Cycles and Triangles in Euler totient Cayley graphs. Graphs Theory Notes of New York LIX (2010), 28-31.
[9]	L.Madhavi, Studies on Domination Parameters and ‘Enumeration of Cycles in some Arithmetic Graphs, Doctoral Thesis, Sri Venkateswara University, Tirupati, India (2002).
[10]	N.Vasumathi, Number Theoretic Graphs, Doctoral Thesis, S.V.University, Tirupati, India (1994).

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APA Style

Levaku Madhavi, Tekuri Chalapathi. (2015). Enumeration of Triangles in Cayley Graphs. Pure and Applied Mathematics Journal, 4(3), 128-132. https://doi.org/10.11648/j.pamj.20150403.21

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ACS Style

Levaku Madhavi; Tekuri Chalapathi. Enumeration of Triangles in Cayley Graphs. Pure Appl. Math. J. 2015, 4(3), 128-132. doi: 10.11648/j.pamj.20150403.21

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AMA Style

Levaku Madhavi, Tekuri Chalapathi. Enumeration of Triangles in Cayley Graphs. Pure Appl Math J. 2015;4(3):128-132. doi: 10.11648/j.pamj.20150403.21

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@article{10.11648/j.pamj.20150403.21,
  author = {Levaku Madhavi and Tekuri Chalapathi},
  title = {Enumeration of Triangles in Cayley Graphs},
  journal = {Pure and Applied Mathematics Journal},
  volume = {4},
  number = {3},
  pages = {128-132},
  doi = {10.11648/j.pamj.20150403.21},
  url = {https://doi.org/10.11648/j.pamj.20150403.21},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20150403.21},
  abstract = {Significant contributions can be found on the study of the cycle structure in graphs, particularly in Cayley graphs. Determination of Hamilton cycles and triangles, the longest and shortest cycles attracts special attention. In this paper an enumeration process for the determination of number of triangles in the Cayley graph associated with a group not necessarily abelian and a symmetric subset of the group.},
 year = {2015}
}

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TY  - JOUR
T1  - Enumeration of Triangles in Cayley Graphs
AU  - Levaku Madhavi
AU  - Tekuri Chalapathi
Y1  - 2015/06/11
PY  - 2015
N1  - https://doi.org/10.11648/j.pamj.20150403.21
DO  - 10.11648/j.pamj.20150403.21
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 128
EP  - 132
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20150403.21
AB  - Significant contributions can be found on the study of the cycle structure in graphs, particularly in Cayley graphs. Determination of Hamilton cycles and triangles, the longest and shortest cycles attracts special attention. In this paper an enumeration process for the determination of number of triangles in the Cayley graph associated with a group not necessarily abelian and a symmetric subset of the group.
VL  - 4
IS  - 3
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Author Information

Levaku Madhavi

Department of Applied Mathematics, Yogi Vemana University, Kadapa, A. P., India
Tekuri Chalapathi

Department of Mathematics, Sree Vidyanikethan Engineering College, A. Rangampet, Tirupati, A. P., India

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APA Style

Levaku Madhavi, Tekuri Chalapathi. (2015). Enumeration of Triangles in Cayley Graphs. Pure and Applied Mathematics Journal, 4(3), 128-132. https://doi.org/10.11648/j.pamj.20150403.21

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ACS Style

Levaku Madhavi; Tekuri Chalapathi. Enumeration of Triangles in Cayley Graphs. Pure Appl. Math. J. 2015, 4(3), 128-132. doi: 10.11648/j.pamj.20150403.21

Copy | Download

AMA Style

Levaku Madhavi, Tekuri Chalapathi. Enumeration of Triangles in Cayley Graphs. Pure Appl Math J. 2015;4(3):128-132. doi: 10.11648/j.pamj.20150403.21

Copy | Download

@article{10.11648/j.pamj.20150403.21,
  author = {Levaku Madhavi and Tekuri Chalapathi},
  title = {Enumeration of Triangles in Cayley Graphs},
  journal = {Pure and Applied Mathematics Journal},
  volume = {4},
  number = {3},
  pages = {128-132},
  doi = {10.11648/j.pamj.20150403.21},
  url = {https://doi.org/10.11648/j.pamj.20150403.21},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20150403.21},
  abstract = {Significant contributions can be found on the study of the cycle structure in graphs, particularly in Cayley graphs. Determination of Hamilton cycles and triangles, the longest and shortest cycles attracts special attention. In this paper an enumeration process for the determination of number of triangles in the Cayley graph associated with a group not necessarily abelian and a symmetric subset of the group.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Enumeration of Triangles in Cayley Graphs
AU  - Levaku Madhavi
AU  - Tekuri Chalapathi
Y1  - 2015/06/11
PY  - 2015
N1  - https://doi.org/10.11648/j.pamj.20150403.21
DO  - 10.11648/j.pamj.20150403.21
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 128
EP  - 132
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20150403.21
AB  - Significant contributions can be found on the study of the cycle structure in graphs, particularly in Cayley graphs. Determination of Hamilton cycles and triangles, the longest and shortest cycles attracts special attention. In this paper an enumeration process for the determination of number of triangles in the Cayley graph associated with a group not necessarily abelian and a symmetric subset of the group.
VL  - 4
IS  - 3
ER  -

Copy | Download