TY - JOUR
ID - 13642
TI - On the signed Roman edge k-domination in graphs
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Mahmoodi, Akram
AD - Department of Mathematics
Payame Noor University
I.R. Iran
Y1 - 2017
PY - 2017
VL - 2
IS - 1
SP - 57
EP - 64
KW - signed Roman edge k-dominating function
KW - signed Roman edge k-domination number
KW - Domination number
DO - 10.22049/cco.2017.25962.1061
N2 - Let $kgeq 1$ be an integer, and $G=(V,E)$ be a finite and simple graph. The closed neighborhood $N_G[e]$ of an edge $e$ in a graph $G$ is the set consisting of $e$ and all edges having a common end-vertex with $e$. A signed Roman edge $k$-dominating function (SREkDF) on a graph $G$ is a function $f:E rightarrow {-1,1,2}$ satisfying the conditions that (i) for every edge $e$ of $G$, $sum _{xin N[e]} f(x)geq k$ and (ii) every edge $e$ for which $f(e)=-1$ is adjacent to at least one edge $e'$ for which $f(e')=2$. The minimum of the values $sum_{ein E}f(e)$, taken over all signed Roman edge $k$-dominating functions $f$ of $G$, is called the signed Roman edge $k$-domination number of $G$ and is denoted by $gamma'_{sRk}(G)$. In this paper we establish some new bounds on the signed Roman edge $k$-domination number.
UR - http://comb-opt.azaruniv.ac.ir/article_13642.html
L1 - http://comb-opt.azaruniv.ac.ir/article_13642_c8b75d7b7cce416e2210ba5e68bb4ee2.pdf
ER -