Connected 2- Dominating Sets and Connected 2- Domination Polynomials of the Complete Bipartite Graph k_(2,m)

Y.A. Shiny, Anithababy T

Abstract


Let  be a simple graph.Let  be the family of connected 2 dominating sets in with cardinality  and |.Then the polynomial is called the 2 domination polynomial of  where is the connected 2  domination number of Let  be the family of connected 2 dominating sets of theComplete bipartite graph  with cardinality  and let .Then the connected 2  domination polynomial   of  is defined as where  is the connected2 – domination number of .In this paper, we obtain a recursive formula for .Using this recursive formula, we construct the connected 2 domination polynomial  is the number of connected 2 dominating sets of  of cardinality  and some properties of this polynomial have been studied

Keywords


Dominating, Connected and cardinality

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References


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DOI: http://dx.doi.org/10.23755/rm.v44i0.889

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