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MEDIUM DOMINATION DECOMPOSITION NUMBER OF JOIN OF GRAPHS

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Saranya J, Ebin Raja Merly E
» doi: 10.53555/ecb/2022.11.03.14

Abstract

The Medium domination Number is a notation which uses neighbourhood of each pair of vertices. If any two adjacent vertices that are dominating each other, then the domination number of that vertices is atleast one. For any connected, undirected, simple graph G of order p, the Medium Domination Number MD(G) =(TDV(G))/(pC_2 ) , where TDV(G) is the total number of vertices that dominate every pair of vertices. A decomposition (G_1,G_2,…,G_(n )) of a graph G is said to be Medium Domination Decomposition (MDD) if ⌊MD(G_i )⌋= i-1,i=1,2,...,n.The number of subgraphs of a Medium Domination Decomposition (G_1,G_2,…,G_(n ) ) of a graph G is said to be Medium Domination Decomposition Number of G and is denoted by π_MD (G). Here, we have investigated some new bounds on Medium Domination Decomposition Number of join of graphs.

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