Volume :8 , Issue :2 ,Page :55-74

Abstract : The Medium domination number of a graph was introduced by Duygu Vargor et,al., in [1]. Motivated by the above in [5], Mahadevan, Vijaya lakshmi and Sivagnanam introduced the concept of extended medium domination number of a graph. Th is concept has lot of application in computer communication networks. edom(u,v) is sum of number of u-v paths of length one, two and three. The total number of vertices that domina te every pair of vertices ETDV(G) =  ) , ( v u edom for u, v  V(G). In any simple graph G of p number of ve rtices, the extended me dium domination number of G is defined as EMD(G)=         2 p ) G ( ETDV . In this paper, we investigat e the extended medium domination number for some special types of graphs.