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Construction of Sc Chordal and Sc Weakly Chordal Graphs

Received: 13 April 2016     Accepted: 18 May 2016     Published: 4 June 2016
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Abstract

Study of any graph class includes characterization, recognition, counting the number of graphs i.e. cataloging and construction of graphs. The construction of sc chordal graphs by mean of complementing permutation is one of the known method. In this paper, a new method for the construction of sc chordal graphs is proposed based on a two-pair of graphs. We also presented algorithm for the construction of sc weakly chordal graphs.

Published in American Journal of Applied Mathematics (Volume 4, Issue 3)
DOI 10.11648/j.ajam.20160403.17
Page(s) 163-168
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), 2016. Published by Science Publishing Group

Keywords

Self-Complementary Graph, Chordal and Weakly Chordal Graph, Two-Pair, Degree Sequence, P4

References
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[2] C. T. Hoang, Brain Moore, D. Roecoskie, J Sawada, M. Vatshelle, Construction of k- critical P5-free graphs, Discrete Applied Mathematics, 182 (2015), 91-98.
[3] D. R. Fulkerson and O. A. Gross, Incidence matrices and interval graphs, Pacafic J. Math., 15 (1965) 835-855.
[4] G. Ringel, Selbstkomplementare Graphen, Arch Math. (Basel), 14 (1963) 354-358.
[5] H. Sachs, Uber selbstkomplementare Graphen, Publ. Math. Debreen, 9 (1962) 270-288.
[6] J. Yellen and J Gross, Graph Theory and its Applications, CRC Press (USA), 1999.
[7] J. Xu and C. K. Wong, Self-complementary graphs and Ramsey numbers Part-1: the decomposition and the construction of self-complementary graphs, Discrete mathematics, 223 (2000) 309-326.
[8] Lihuan Mao, Fenjin Liu, Wei Wang, A new method for the constructing graphs determined by their generalized spectrum, Linear Algebra and its Applications, 477 (2015) 112-127.
[9] M. R. Sridharan and K. Balaji, Characterisation of self-complementary chordal graphs, Discrete Mathematics, 188 (1998) 279-283.
[10] M. R. Sridharan and K. Balaji, On construction of self-complementary chordal graphs, Journal of Combinatorics Information and system sciences, 24 (1999) 39-45.
[11] R. A. Gibbs, Self-Complementary Graphs, J. Comb. Theory Series B, 16 (1974) 106-123.
[12] R. B. Hayward, Generating weakly triangulated graphs, J. Graph Theory, 21 (1996) 67-70.
[13] Xueyi Huang and Qiongxiang Huang Construction of graphs with exactly k main eigenvalues, Linear Algebra and its Applications, 486 (2015), 204-218
Cite This Article
  • APA Style

    Parvez Ali, Syed Ajaz Kareem Kirmani. (2016). Construction of Sc Chordal and Sc Weakly Chordal Graphs. American Journal of Applied Mathematics, 4(3), 163-168. https://doi.org/10.11648/j.ajam.20160403.17

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    ACS Style

    Parvez Ali; Syed Ajaz Kareem Kirmani. Construction of Sc Chordal and Sc Weakly Chordal Graphs. Am. J. Appl. Math. 2016, 4(3), 163-168. doi: 10.11648/j.ajam.20160403.17

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    AMA Style

    Parvez Ali, Syed Ajaz Kareem Kirmani. Construction of Sc Chordal and Sc Weakly Chordal Graphs. Am J Appl Math. 2016;4(3):163-168. doi: 10.11648/j.ajam.20160403.17

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  • @article{10.11648/j.ajam.20160403.17,
      author = {Parvez Ali and Syed Ajaz Kareem Kirmani},
      title = {Construction of Sc Chordal and Sc Weakly Chordal Graphs},
      journal = {American Journal of Applied Mathematics},
      volume = {4},
      number = {3},
      pages = {163-168},
      doi = {10.11648/j.ajam.20160403.17},
      url = {https://doi.org/10.11648/j.ajam.20160403.17},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20160403.17},
      abstract = {Study of any graph class includes characterization, recognition, counting the number of graphs i.e. cataloging and construction of graphs. The construction of sc chordal graphs by mean of complementing permutation is one of the known method. In this paper, a new method for the construction of sc chordal graphs is proposed based on a two-pair of graphs. We also presented algorithm for the construction of sc weakly chordal graphs.},
     year = {2016}
    }
    

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    T1  - Construction of Sc Chordal and Sc Weakly Chordal Graphs
    AU  - Parvez Ali
    AU  - Syed Ajaz Kareem Kirmani
    Y1  - 2016/06/04
    PY  - 2016
    N1  - https://doi.org/10.11648/j.ajam.20160403.17
    DO  - 10.11648/j.ajam.20160403.17
    T2  - American Journal of Applied Mathematics
    JF  - American Journal of Applied Mathematics
    JO  - American Journal of Applied Mathematics
    SP  - 163
    EP  - 168
    PB  - Science Publishing Group
    SN  - 2330-006X
    UR  - https://doi.org/10.11648/j.ajam.20160403.17
    AB  - Study of any graph class includes characterization, recognition, counting the number of graphs i.e. cataloging and construction of graphs. The construction of sc chordal graphs by mean of complementing permutation is one of the known method. In this paper, a new method for the construction of sc chordal graphs is proposed based on a two-pair of graphs. We also presented algorithm for the construction of sc weakly chordal graphs.
    VL  - 4
    IS  - 3
    ER  - 

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Author Information
  • College of Engineering, Unayzah, Qassim University, Al-Qassim, Kingdom of Saudi Arabia

  • College of Engineering, Unayzah, Qassim University, Al-Qassim, Kingdom of Saudi Arabia

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