Fractional Domination for Two Classes of Graphs

Baogen Xu; Yan Zou; Lixin Zhao

doi:doi:10.11648/j.pamj.20140306.15

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Fractional Domination for Two Classes of Graphs

Baogen Xu, Yan Zou, Lixin Zhao

Published in Pure and Applied Mathematics Journal (Volume 3, Issue 6)

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

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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), 2024. 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.

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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

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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

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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

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@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}
}

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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  -

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Author Information

Baogen Xu

School of Natural Science, East China Jiaotong University, Nanchang, 330013, China
Yan Zou

School of Natural Science, East China Jiaotong University, Nanchang, 330013, China
Lixin Zhao

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

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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

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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

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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