NONSPLIT PENDANT DOMINATION IN GRAPHS

Résumé

Abstract. For a graph G, a dominating set S in G is called a pendant domi-
nating set if the hSi contains at least one pendant vertex. The least cardinality
of the pendant dominating set in G is called the pendant domination number of G, denoted by pe(G). A pendant dominating set S of a graph G is a nonsplit pendant dominating set if the induced graph < V -S > is connected. The nonsplit pendant domination number, denoted by nsp(G) is the minimum cardinality of a nonsplit pendant domination set. In this several bounds on  nonsplit pendant domination number,  are established, and exact values are determined for some standard graphs. Additionally, its relationship with other domination parameters
is investigated.