| Peer-Reviewed

Enumeration of Triangles in Cayley Graphs

Received: 12 May 2015     Accepted: 23 May 2015     Published: 11 June 2015
Views:       Downloads:
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).
Cite This Article
  • 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

    Copy | Download

    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

Author Information
  • Department of Applied Mathematics, Yogi Vemana University, Kadapa, A. P., India

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

  • Sections