Signed Total Domatic Number of Directed Circulant Graphs

A function f : V(D) → {−1, 1} is a signed total dominating function (STDF) of a directed graph D, if
forevery vertex v ∈ V, (
( )) ∑ ∈ ( ) ( ) . A STDF of a directed graph D is said to be
SETDF iffor every vertex v ∈ V, (
( )) = 1 when |
( )| is odd and (
( )) = 2 when |
( )| is
even. Westudy some properties of signed total domatic number (D) in directed circulant graphs. We
characterizesome classes of directed circulant graphs for which ( ) =
( ) . Further, we find a
necessary andsufficient condition for the existence of SETDF in a family of directed circulant graphs in
terms of coveringprojection