Twin signed domination numbers in directed graphs

Abstract

Let D = (V, A) be a finite simple directed graph (shortly digraph). A function f : V −→ {−1, 1} is called a twin signed dominating function (TSDF) if f(N −[v]) > 1 and f(N +[v]) > 1 for each vertex v ∈ V . The twin signed domination number of D is γ∗s(D) = min{ω(f) | f is a TSDF of D}. In this paper, we initiate the study of twin signed domination in digraphs and we present sharp lower bounds for γ∗s (D) in terms of the order, size and maximum and minimum indegrees and outdegrees. Some of our results are extensions of well-known lower bounds of the classical signed domination numbers of graphs.