Study of graph partitions approach satisfies vizing's conjecture
Other Title(s)
دراسة طريقة تجزيء للبيان تحقق تخمين فيزنج
Author
Source
Tishreen University Journal for Research and Scientific Studies : Basic Sciences Series
Issue
Vol. 39, Issue 3 (30 Jun. 2017), pp.231-236, 6 p.
Publisher
Publication Date
2017-06-30
Country of Publication
Syria
No. of Pages
6
Main Subjects
Abstract EN
For a graph G(V,E) , a subset of vertices D is a dominating set if for each vertex 12x∈"> V either 12x∈D"> , or x is adjacent to at least one vertex of D .
The domination number , 12خ³G, "> is the order of smallest dominating set of G .
In [7], Vizing conjectured that 12خ³Gأ—H ≥ خ³Gأ—خ³H"> for any two graphs G and H , where G×H denotes their Cartesian product .
This conjecture is still open .
In this paper , we investigate following relations, if a graph H has a D-partition then it also has a K-partition, and if H has a K-partition , then Vizing's conjecture is satisfied for any graph G , after that, every cycle 12Cn , n≥3"> , has a K-partition.
Moreover, if H has a K-partition , then H satisfies the following relations 12خ³H≤2"> , 12P2H=خ³H"> and H is a perfect-dominated graph .
American Psychological Association (APA)
Muhammad, Jamil. 2017. Study of graph partitions approach satisfies vizing's conjecture. Tishreen University Journal for Research and Scientific Studies : Basic Sciences Series،Vol. 39, no. 3, pp.231-236.
https://search.emarefa.net/detail/BIM-849378
Modern Language Association (MLA)
Muhammad, Jamil. Study of graph partitions approach satisfies vizing's conjecture. Tishreen University Journal for Research and Scientific Studies : Basic Sciences Series Vol. 39, no. 3 (2017), pp.231-236.
https://search.emarefa.net/detail/BIM-849378
American Medical Association (AMA)
Muhammad, Jamil. Study of graph partitions approach satisfies vizing's conjecture. Tishreen University Journal for Research and Scientific Studies : Basic Sciences Series. 2017. Vol. 39, no. 3, pp.231-236.
https://search.emarefa.net/detail/BIM-849378
Data Type
Journal Articles
Language
English
Notes
Record ID
BIM-849378