Cototal edge domination number of a graph
S. B. Anupama, Y. B. Maralabhavi, Venkanagouda M Goudar · Malaya Journal of Matematik · 2016
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 $\gamma^{\prime}(G)$ 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 $\gamma_{c o t}^{\prime}(G)$. We investigate several properties of cototal edge dominating sets and give some bounds on the cototal edge domination number.