Geodesic
On The Co-Roman Domination in Graphs
Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 2, pp. 455-472

Voir la notice de l'article provenant de la source Library of Science

Let G = (V, E) be a graph and let f : V (G) →0, 1, 2 be a function. A vertex v is said to be protected with respect to f, if f(v) gt; 0 or f(v) = 0 and v is adjacent to a vertex of positive weight. The function f is a co-Roman dominating function if (i) every vertex in V is protected, and (ii) each v ∈ V with positive weight has a neighbor u ∈ V with f(u) = 0 such that the function f_uv : V →0, 1, 2, defined by f_uv (u) = 1, f_uv(v) = f(v) − 1 and f_uv(x) = f(x) for x ∈ V \{ v, u }, has no unprotected vertex. The weight of f is ω(f) = Σ_ v ∈ V f(v). The co-Roman domination number of a graph G, denoted by γ_cr(G), is the minimum weight of a co-Roman dominating function on G. In this paper, we give a characterization of graphs of order n for which co-Roman domination number is 2n3 or n − 2, which settles two open problem in [S. Arumugam, K. Ebadi and M. Manrique, Co-Roman domination in graphs, Proc. Indian Acad. Sci. Math. Sci. 125 (2015) 1–10]. Furthermore, we present some sharp bounds on the co-Roman domination number.
Keywords: co-Roman dominating function, co-Roman domination number, Roman domination 
@article{DMGT_2019_39_2_a10,
     author = {Shao, Zehui and Sheikholeslami, Seyed Mahmoud and Soroudi, Marzieh and Volkmann, Lutz and Liu, Xinmiao},
     title = {On {The} {Co-Roman} {Domination} in {Graphs}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {455--472},
     publisher = {mathdoc},
     volume = {39},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2019_39_2_a10/}
}
TY  - JOUR
AU  - Shao, Zehui
AU  - Sheikholeslami, Seyed Mahmoud
AU  - Soroudi, Marzieh
AU  - Volkmann, Lutz
AU  - Liu, Xinmiao
TI  - On The Co-Roman Domination in Graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2019
SP  - 455
EP  - 472
VL  - 39
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2019_39_2_a10/
LA  - en
ID  - DMGT_2019_39_2_a10
ER  - 
%0 Journal Article
%A Shao, Zehui
%A Sheikholeslami, Seyed Mahmoud
%A Soroudi, Marzieh
%A Volkmann, Lutz
%A Liu, Xinmiao
%T On The Co-Roman Domination in Graphs
%J Discussiones Mathematicae. Graph Theory
%D 2019
%P 455-472
%V 39
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2019_39_2_a10/
%G en
%F DMGT_2019_39_2_a10
Shao, Zehui; Sheikholeslami, Seyed Mahmoud; Soroudi, Marzieh; Volkmann, Lutz; Liu, Xinmiao. On The Co-Roman Domination in Graphs. Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 2, pp. 455-472. http://geodesic.mathdoc.fr/item/DMGT_2019_39_2_a10/