Introduction to Transversal Pendant Domination in Graphs

Authors: Nayaka S.R., Putta Swamy, Purushothama S.

Abstract:

Let G=(V, E) be a graph. A dominating set S in G is a pendant dominating set if < S > contains a pendant vertex. A pendant dominating set of G which intersects every minimum pendant dominating set in G is called a transversal pendant dominating set. The minimum cardinality of a transversal pendant dominating set is called the transversal pendant domination number of G, denoted by γ_tp(G). In this paper, we begin to study this parameter. We calculate γ_tp(G) for some families of graphs. Furthermore, some bounds and relations with other domination parameters are obtained for γ_tp(G).

Keywords: dominating set, pendant dominating set, pendant domination number, transversal pendant dominating set, transversal pendant domination number