1Department of Mathematics, Azarbaijan Shahid Madani University Tabriz 2Department of Mathematics, Gareziaeddin Center, Khoy Branch, Islamic Azad University, Khoy 3Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. 4Lehrstuhl II fur Mathematik, RWTH Aachen University, 52056 Aachen, Germany
Acta mathematica Universitatis Comenianae, Tome 87 (2018) no. 1, pp. 1-13
Citer cet article
R. Khoeilar; H. Aram; S. M. Sheikholeslami; L. Volkmann; R. Khoeilar; H. Aram; S. M. Sheikholeslami; L. Volkmann. Relating the annihilation number and the Roman domination. Acta mathematica Universitatis Comenianae, Tome 87 (2018) no. 1, pp. 1-13. http://geodesic.mathdoc.fr/item/AMUC_2018_87_1_a0/
@article{AMUC_2018_87_1_a0,
author = {R. Khoeilar and H. Aram and S. M. Sheikholeslami and L. Volkmann and R. Khoeilar and H. Aram and S. M. Sheikholeslami and L. Volkmann},
title = { Relating the annihilation number and the {Roman} domination},
journal = {Acta mathematica Universitatis Comenianae},
pages = {1--13},
year = {2018},
volume = {87},
number = {1},
url = {http://geodesic.mathdoc.fr/item/AMUC_2018_87_1_a0/}
}
TY - JOUR
AU - R. Khoeilar
AU - H. Aram
AU - S. M. Sheikholeslami
AU - L. Volkmann
AU - R. Khoeilar
AU - H. Aram
AU - S. M. Sheikholeslami
AU - L. Volkmann
TI - Relating the annihilation number and the Roman domination
JO - Acta mathematica Universitatis Comenianae
PY - 2018
SP - 1
EP - 13
VL - 87
IS - 1
UR - http://geodesic.mathdoc.fr/item/AMUC_2018_87_1_a0/
ID - AMUC_2018_87_1_a0
ER -
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%A H. Aram
%A S. M. Sheikholeslami
%A L. Volkmann
%A R. Khoeilar
%A H. Aram
%A S. M. Sheikholeslami
%A L. Volkmann
%T Relating the annihilation number and the Roman domination
%J Acta mathematica Universitatis Comenianae
%D 2018
%P 1-13
%V 87
%N 1
%U http://geodesic.mathdoc.fr/item/AMUC_2018_87_1_a0/
%F AMUC_2018_87_1_a0
A {\em Roman dominating function} (RDF) on a graph $G$ is a labeling$f\:$V (G)\rightarrow \{0, 1, 2\}$ such that every vertex withlabel 0 has a neighbor with label 2. The {\em weight} of an RDF$f$ is the value $\omega(f)=\sum_{v\in V}f (v)$. The {\em Romandomination number} of a graph $G$, denoted by $\gamma_R(G)$,equals the minimum weight of an RDF on G. The annihilation number$a(G)$ is the largest integer $k$ such that the sum of the first$k$ terms of the non-decreasing degree sequence of $G$ is at mostthe number of edges in $G$. In this paper, we prove that for anytree $T$ of order at least two, $\gamma_{R}(T)\le\frac{4a(T)+2}{3}$.
