On restrained edge dominating set of graphs
Authors :
S. K. Vaidya 1 * and P. D. Ajani 2
Author Address :
1 Department of Mathematics, Saurashtra University, Rajkot-360005, Gujarat, India.
2 Department of Mathematics,, Atmiya University, Rajkot - 360005, Gujarat, India.
*Corresponding author.
Abstract :
For a graph $G=(V,E)$, a subset $D$ of $E$ is restrained edge dominating set of $G$ if every edge not in $D$ is adjacent to an edge in $D$ as well as an edge in $E-D$. The restrained edge domination number of $G$, denoted by $\gamma_{re}(G)$ is the minimum cardinality of a restrained edge dominating set of $G$. Here, we characterize restrained edge dominating set and also investigate restrained edge domination number of some wheel related graphs.
Keywords :
Dominating set, restrained dominating set, restrained edge dominating set, restrained edge domination number.
DOI :
Article Info :
Received : October 11, 2019; Accepted : November 27, 2019.
