Abstract

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

Keywords and Phrases

Antipodal Domination, Diameter.

A.M.S. subject classification

05C69.

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