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 γs*(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 γs*(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.