2-Domination Number of Butterfly Graphs

Papandangal Vijaya Jyothi; Bommireddy Maheswari; Indrani Kelkar

Authors

Papandangal Vijaya Jyothi
Bommireddy Maheswari
Indrani Kelkar

Keywords:

Butterfly Graphs, Dominating set, 2-Dominating set

Abstract

A new family of graphs called Butterfly Graphs is introduced recently and study of its parameters is under progress. Butterfly Graphs are undirected graphs and are widely used in interconnection networks. In this paper, we find 2-dominating sets of Butterfly graph and show that 2-domination number of $gif.latex?BF(n)$ is

$gif.latex?\begin{array}{ll}&space;\gamma_{\times&space;2}(BF(n))=2^{n}&space;&&space;\text{if&space;}&space;n=2&space;\\&space;\gamma_{\times&space;2}(BF(n))=k&space;\times&space;2^{n}&space;+r&space;\times&space;2^{n-1}&space;&&space;\text{if&space;}&space;n=3k+r.&space;\end{array}$

2-Domination Number of Butterfly Graphs

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