| Peer-Reviewed

Fractional Domination for Two Classes of Graphs

Received: 15 November 2014     Accepted: 27 December 2014     Published: 4 January 2015
Views:       Downloads:
Abstract

Let be a graph, a real-valued function is said to be a dominating of G if holds for every vertex, the fractional domination function number is defined as, and the fractional total domination function number of G is analogous. In this paper we research the fractional domination problem for two classes of special graphs, obtained the fractional domination numbers of the generalized star graphs and the fractional total domination function numbers of the generalized wheel graphs.

Published in Pure and Applied Mathematics Journal (Volume 3, Issue 6)
DOI 10.11648/j.pamj.20140306.15
Page(s) 137-139
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

Generalized Wheel Graph, Fractional Domination Function Number, Fractional Total Domination Number, Generalized Star Graph

References
[1] Baogen Xu. Theory of domination and coloring in graphs. Huazhong university of science and technology press, Wuhan, 2013
[2] Xiandi Zhang, Zhengliang Li. Graphs theory and its applications [M]. Peking: Higher education press,2005
[3] Bondy J A, Murty V S R. Graph theory with applications [M]. New York: Elsevier, 1976.
[4] G S Domke, S T Hedetniemi, R C Laskar. Fractional packings, coverings and irredundance in graphs [J]. Congr. Numer., 1988, 66: 227-238.
[5] T W Haynes, S T Hedetniemi, P J Slater. Domination in Graphs [M]. New York: Marcel Dekker Inc.1998.
Cite This Article
  • APA Style

    Baogen Xu, Yan Zou, Lixin Zhao. (2015). Fractional Domination for Two Classes of Graphs. Pure and Applied Mathematics Journal, 3(6), 137-139. https://doi.org/10.11648/j.pamj.20140306.15

    Copy | Download

    ACS Style

    Baogen Xu; Yan Zou; Lixin Zhao. Fractional Domination for Two Classes of Graphs. Pure Appl. Math. J. 2015, 3(6), 137-139. doi: 10.11648/j.pamj.20140306.15

    Copy | Download

    AMA Style

    Baogen Xu, Yan Zou, Lixin Zhao. Fractional Domination for Two Classes of Graphs. Pure Appl Math J. 2015;3(6):137-139. doi: 10.11648/j.pamj.20140306.15

    Copy | Download

  • @article{10.11648/j.pamj.20140306.15,
      author = {Baogen Xu and Yan Zou and Lixin Zhao},
      title = {Fractional Domination for Two Classes of Graphs},
      journal = {Pure and Applied Mathematics Journal},
      volume = {3},
      number = {6},
      pages = {137-139},
      doi = {10.11648/j.pamj.20140306.15},
      url = {https://doi.org/10.11648/j.pamj.20140306.15},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20140306.15},
      abstract = {Let be a graph, a real-valued function is said to be a dominating of G if holds for every vertex, the fractional domination function number is defined as, and the fractional total domination function number of G is analogous. In this paper we research the fractional domination problem for two classes of special graphs, obtained the fractional domination numbers of the generalized star graphs and the fractional total domination function numbers of the generalized wheel graphs.},
     year = {2015}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Fractional Domination for Two Classes of Graphs
    AU  - Baogen Xu
    AU  - Yan Zou
    AU  - Lixin Zhao
    Y1  - 2015/01/04
    PY  - 2015
    N1  - https://doi.org/10.11648/j.pamj.20140306.15
    DO  - 10.11648/j.pamj.20140306.15
    T2  - Pure and Applied Mathematics Journal
    JF  - Pure and Applied Mathematics Journal
    JO  - Pure and Applied Mathematics Journal
    SP  - 137
    EP  - 139
    PB  - Science Publishing Group
    SN  - 2326-9812
    UR  - https://doi.org/10.11648/j.pamj.20140306.15
    AB  - Let be a graph, a real-valued function is said to be a dominating of G if holds for every vertex, the fractional domination function number is defined as, and the fractional total domination function number of G is analogous. In this paper we research the fractional domination problem for two classes of special graphs, obtained the fractional domination numbers of the generalized star graphs and the fractional total domination function numbers of the generalized wheel graphs.
    VL  - 3
    IS  - 6
    ER  - 

    Copy | Download

Author Information
  • School of Natural Science, East China Jiaotong University, Nanchang, 330013, China

  • School of Natural Science, East China Jiaotong University, Nanchang, 330013, China

  • School of Natural Science, East China Jiaotong University, Nanchang, 330013, China

  • Sections