Cototal Edge Domination Number of a Graph
Authors :
Anupama S.B.a,* Y. B. Maralabhavib and Venkanagouda M. Goudarc
Author Address :
aResearch Scholar, Department of Mathematics, Bangalore University, Bengaluru- 560001, Karnataka, India.
bDepartment of Mathematics, Bangalore University, Bengaluru- 560001, Karnataka, India.
cDepartment of Mathematics, Sri Siddhartha Institute of Technology, Tumkur -572105, Karnataka, India.
*Corresponding author.
Abstract :
A set $F$ of a graph $G(V,E)$ is an edge dominating set if every edge in $E-F$ is adjacent to some edge in $F$. An edge domination number $\gamma^{’}(G)$ of $G$ is the minimum cardinality of an edge dominating set. An edge dominating set $F$ is called a cototal edge dominating set if the induced subgraph $\langle E - F \rangle$ doesnot contain isolated edge. The minimum cardinality of the cototal edge dominating set in $G$ is its domination number and is denoted by $\gamma^{’}_{cot}(G)$. We investigate several properties of cototal edge dominating sets and give some bounds on the cototal edge domination number.
Keywords :
Edge domination number, cototal edge domination number.
DOI :
Article Info :
Received : October 10, 2015; Accepted : April 09, 2016.