Cototal Edge Domination Number of a Graph

Anupama S.B.a,* Y. B. Maralabhavib and Venkanagouda M. Goudarc

Cototal Edge Domination Number of a Graph

Authors :

Anupama S.B.^a,* Y. B. Maralabhavi^band Venkanagouda M. Goudar^c

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.