TY - JOUR
ID - 13654
TI - Roman domination excellent graphs: trees
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Samodivkin, Vladimir D.
AD - University of Architecture, Civil Đ•ngineering and Geodesy;
Department of Mathematics
Y1 - 2018
PY - 2018
VL - 3
IS - 1
SP - 1
EP - 24
KW - Roman domination number
KW - excellent graphs
KW - trees
DO - 10.22049/cco.2017.25806.1041
N2 - A Roman dominating function (RDF) on a graph $G = (V, E)$ is a labeling $f : V rightarrow {0, 1, 2}$ suchthat every vertex with label $0$ has a neighbor with label $2$. The weight of $f$ is the value $f(V) = Sigma_{vin V} f(v)$The Roman domination number, $gamma_R(G)$, of $G$ is theminimum weight of an RDF on $G$.An RDF of minimum weight is called a $gamma_R$-function.A graph G is said to be $gamma_R$-excellent if for each vertex $x in V$there is a $gamma_R$-function $h_x$ on $G$ with $h_x(x) not = 0$. We present a constructive characterization of $gamma_R$-excellent trees using labelings. A graph $G$ is said to be in class $UVR$ if $gamma(G-v) = gamma (G)$ for each $v in V$, where $gamma(G)$ is the domination number of $G$. We show that each tree in $UVR$ is $gamma_R$-excellent.
UR - http://comb-opt.azaruniv.ac.ir/article_13654.html
L1 - http://comb-opt.azaruniv.ac.ir/article_13654_ec8df599ae3874367c247f6fb520698c.pdf
ER -