Signed Total Roman Domination in Digraphs

Lutz Volkmann. "Signed Total Roman Domination in Digraphs." Discussiones Mathematicae Graph Theory 37.1 (2017): 261-272. <http://eudml.org/doc/288020>.

@article{LutzVolkmann2017,
abstract = {Let D be a finite and simple digraph with vertex set V (D). A signed total Roman dominating function (STRDF) on a digraph D is a function f : V (D) → \{−1, 1, 2\} satisfying the conditions that (i) ∑x∈N−(v) f(x) ≥ 1 for each v ∈ V (D), where N−(v) consists of all vertices of D from which arcs go into v, and (ii) every vertex u for which f(u) = −1 has an inner neighbor v for which f(v) = 2. The weight of an STRDF f is w(f) = ∑v∈V (D) f(v). The signed total Roman domination number γstR(D) of D is the minimum weight of an STRDF on D. In this paper we initiate the study of the signed total Roman domination number of digraphs, and we present different bounds on γstR(D). In addition, we determine the signed total Roman domination number of some classes of digraphs. Some of our results are extensions of known properties of the signed total Roman domination number γstR(G) of graphs G.},
author = {Lutz Volkmann},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {digraph; signed total Roman dominating function; signed total Roman domination number},
language = {eng},
number = {1},
pages = {261-272},
title = {Signed Total Roman Domination in Digraphs},
url = {http://eudml.org/doc/288020},
volume = {37},
year = {2017},
}

TY - JOUR
AU - Lutz Volkmann
TI - Signed Total Roman Domination in Digraphs
JO - Discussiones Mathematicae Graph Theory
PY - 2017
VL - 37
IS - 1
SP - 261
EP - 272
AB - Let D be a finite and simple digraph with vertex set V (D). A signed total Roman dominating function (STRDF) on a digraph D is a function f : V (D) → {−1, 1, 2} satisfying the conditions that (i) ∑x∈N−(v) f(x) ≥ 1 for each v ∈ V (D), where N−(v) consists of all vertices of D from which arcs go into v, and (ii) every vertex u for which f(u) = −1 has an inner neighbor v for which f(v) = 2. The weight of an STRDF f is w(f) = ∑v∈V (D) f(v). The signed total Roman domination number γstR(D) of D is the minimum weight of an STRDF on D. In this paper we initiate the study of the signed total Roman domination number of digraphs, and we present different bounds on γstR(D). In addition, we determine the signed total Roman domination number of some classes of digraphs. Some of our results are extensions of known properties of the signed total Roman domination number γstR(G) of graphs G.
LA - eng
KW - digraph; signed total Roman dominating function; signed total Roman domination number
UR - http://eudml.org/doc/288020
ER -