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On signed arc total domination in digraphs

Asgharsharghi L., Khodkar A., Sheikholeslami S. M.

Opuscula Mathematica

2018

Vol. 38, no. 6

779--794

Let D = (V, A) be a finite simple digraph and N(uv) = {u'v' ≠ uv | u = u' or v = v'} be the open neighbourhood of uv in D. A function ƒ : A → { — 1, +1} is said to be a signed arc total dominating function (SATDF) of D if [formula] holds for every arc uv ∈ A. The signed arc total domination number [formula] is defined as [formula]. In this paper we initiate the study of the signed arc total domination in digraphs and present some lower bounds for this parameter.