TY - JOUR
ID - 13997
TI - Total Roman domination subdivision number in graphs
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - amjadi, Jafar
AD - Azarbaijan Shahid Madani University
Y1 - 2020
PY - 2020
VL - 5
IS - 2
SP - 157
EP - 168
KW - total Roman domination
KW - total Roman domination subdivision
KW - graph
DO - 10.22049/cco.2020.26470.1117
N2 - A Roman dominating function on a graph $G$ is a function $f:V(G)rightarrow {0,1,2}$ satisfying the condition that every vertex $u$ for which $f(u)=0$ is adjacent to at least one vertex $v$ for which $f(v)=2$. A total Roman dominating function is a Roman dominating function with the additional property that the subgraph of $G$ induced by the set of all vertices of positive weight has no isolated vertices. The weight of a total Roman dominating function $f$ is the value $Sigma_{uin V(G)}f(u)$. The total Roman domination number of $G$, $gamma_{tR}(G)$, is the minimum weight of a total Roman dominating function on $G$. The total Roman domination subdivision number ${rm sd}_{gamma_{tR}}(G)$ of a graph $G$ is the minimum number of edges that must be subdivided (each edge in $G$ can be subdivided at most once) in order to increase the total Roman domination number. In this paper, we initiate the study of total Roman domination subdivision number in graphs and we present sharp bounds for this parameter.
UR - http://comb-opt.azaruniv.ac.ir/article_13997.html
L1 - http://comb-opt.azaruniv.ac.ir/article_13997_361f34d42a9e4c4eeb3798140a18ae6f.pdf
ER -