Strong Efficient Domination Number for Trees and Lict Graphs

Abstract

For a subgraph of a vertex set of a graph to be strong efficient, all remaining vertices in the graph must have exactly one neighbor of equal or greater degree in the specified subgraph and all vertices in the specified subgraph are independent of each other. The strong efficient domination number is the cardinality of such set with the fewest elements. In this paper we obtain many exact values and some bounds regarding this parameter of some trees and their lict graphs.