Pendant Domination in Graphs

Let \(G\) be any graph. The concept of paired domination was introduced having gaurd backup concept in mind. We introduce pendant domination concept, for which at least one guard is assigned a backup, A dominating set \(S\) in \(G\) is called a pendant dominating set if \((S)\) contains at least one pendant vertex. The least cardinality of a pendant dominating set is called the pendant domination number of G denoted by \(\gamma_{pe}(G)\). In this article, we initiate the study of this parameter. The exact value of \(\gamma_{pe}(G)\) for some families of standard graphs are obtained and some bounds are estimated. We also study the proprties of the parameter and interrelation with other invarients.