Paper Title
A Constructive Characterization of Trees with the Same Distance-2 Domination Number
Abstract
The distance between two vertices u and v in a graph G equalsthe length of a shortest path from u to v . A set
D of verticesis distance-2 dominating if every vertex not belonging to D is atdistance at most two of a vertex in D .The
distance-2 domination number of a graph G , denoted by ( ) 2 G , is the minimum cardinality of adistance-2 dominating
setinG .Notethat in general to determine the number ( ) 2 G in a graph Gis NP-complete even if G is bipartite [4]. Here we
focus on the trees. For n 1 , let (n) be the set of trees T satisfying (T) n 2 . In thispaper, we provide a constructive
characterization of (n) for all n 1.