Study of Graph Partitions Approach satisfies Vizing's Conjecture

Authors

  • Jameel Mohammad

Abstract

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 .

 

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Published

2019-02-27

How to Cite

1.
Mohammad J. Study of Graph Partitions Approach satisfies Vizing’s Conjecture. TUJ-BA [Internet]. 2019Feb.27 [cited 2024May2];39(3). Available from: https://journal.tishreen.edu.sy/index.php/bassnc/article/view/3780

Issue

Vol. 39 No. 3 (2017): العلوم الأساسية

Section

Articles

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