Abstract: A set D of
edges is a total edge dominating set of G,
if every edge in G is adjacent to at
least one edge in D. The total edge
domination number is defined to be the minimum number
of edges in a total edge dominating set of G. A set D of edges is an n-total
edge dominating set of G if every edge
in G is adjacent to at least n-edges
in D. The n-total edge domination number is defined to be the minimum number
of edges in an n-total edge dominating
set of G. In this paper, we initiate a
study of n-total edge dominating set
and in particular, we establish some results concerning the n-total
edge domination number of G and also
we establish Nordhaus-Gaddum type result for an n-total
edge domination number of a graph.
Keywords and phrases: edge domination, total edge domination, n-total domination, n-total edge domination.
