ANTIPODAL DOMINATION NUMBER OF GRAPHS

Abstract

A dominating set S  V  is said to be an Antipodal Dominating Set(ADS) of  a  connected  graph  G  if  there  exist  vertices  x, y      S  such  that d(x, y)  =  diam(G).  The  minimum  cardinality  of  an  ADS  is  called  the Antipodal Domination Number(ADN), and is  denoted  by  γ_ap(G).  In  this paper, we determined the antipodal domination number for various graph prod- ucts, bound for antipodal domination and characterize the graphs with γ_ap(G) = 2.