@article {
author = {Mahmoodi, Akram},
title = {On the signed Roman edge k-domination in graphs},
journal = {Communications in Combinatorics and Optimization},
volume = {2},
number = {1},
pages = {57-64},
year = {2017},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2017.25962.1061},
abstract = {Let $k\geq 1$ 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 $G$, $\sum _{x\in N[e]} f(x)\geq k$ 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 $\sum_{e\in E}f(e)$, 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.},
keywords = {signed Roman edge k-dominating function,signed Roman edge k-domination number,Domination number},
url = {http://comb-opt.azaruniv.ac.ir/article_13642.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_13642_c8b75d7b7cce416e2210ba5e68bb4ee2.pdf}
}