A note on the edge Roman domination in trees
| Main Author: | Jafari Rad, Nader; Department of Mathematics Shahrood University of Technology Shahrood, Iran |
|---|---|
| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2017
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| Subjects: | |
| Online Access: |
http://www.ejgta.org/index.php/ejgta/article/view/234 http://www.ejgta.org/index.php/ejgta/article/view/234/pdf_30 http://www.ejgta.org/index.php/ejgta/article/downloadSuppFile/234/51 http://www.ejgta.org/index.php/ejgta/article/downloadSuppFile/234/52 |
Daftar Isi:
- A subset $X$ of edges of a graph $G$ is called an \textit{edgedominating set} of $G$ if every edge not in $X$ is adjacent tosome edge in $X$. The edge domination number $\gamma'(G)$ of $G$ is the minimum cardinality taken over all edge dominating sets of $G$. An \textit{edge Roman dominating function} of a graph $G$ is a function $f : E(G)\rightarrow \{0,1,2 \}$ such that every edge$e$ with $f(e)=0$ is adjacent to some edge $e'$ with $f(e') = 2.$The weight of an edge Roman dominating function $f$ is the value$w(f)=\sum_{e\in E(G)}f(e)$. The edge Roman domination number of $G$, denoted by $\gamma_R'(G)$, is the minimum weight of an edge Roman dominating function of $G$. In this paper, we characterize trees with edge Roman domination number twice the edge domination number.