Format of Original
AKCE International Journal of Graphs and Combinatorics
Recently. Hedetniemi et aI. introduced (1,2)-domination in graphs, and the authors extended that concept to (1, 2)-domination graphs of digraphs. Given vertices x and y in a digraph D, x and y form a (1,2)-dominating pair if and only if for every other vertex z in D, z is one step away from x or y and at most two steps away from the other. The (1,2)-dominating graph of D, dom1,2 (D), is defined to be the graph G = (V, E ) , where V (G) = V (D), and xy is an edge of G whenever x and y form a (1,2)-dominating pair in D. In this paper, we characterize all connected graphs that can be (I, 2)-dominating graphs of tournaments.
Factor, Kim A. S. and Langley, Larry J., "A Characterization of Connected (1,2)-Domination Graphs of Tournaments" (2011). Mathematics, Statistics and Computer Science Faculty Research and Publications. 112.