Eccentric domination number of some path related graphs

Abstract

In a graph \(G\), a vertex \(u\) is said to be an eccentric vertex of a vertex \(v\) if \(d(u, v)=\) eccentricity of vertex \(v\). A dominating set \(D\) of a graph \(G=(V, E)\) is said to be an eccentric dominating set if for every \(v \in V-D\), there exists at least one eccentric vertex of \(v\) in \(D\). The minimum cardinality of the minimal eccentric dominating sets of graph \(G\) is said to be eccentric domination number of graph \(G\) which is denoted by \(\gamma_{e d}(G)\). Here, exact value of \(\gamma_{e d}(G)\) for some path related graphs, have been investigated.