Abstract:
A subset D of the vertex set of a connected graph
G is called a total global neighbourhood dominating set(tgnd-set)
of G if and only if D is a total dominating set of G as well as
GN , where GN is the neighbourhood graph of G. The total global
neighbourhood domination number(tgnd-number) is the minimum
cardinality of a total global neighbourhood dominating set of G
and is denoted by γtgn(G). In this paper sharp bounds for γtgn
are obtained. Exact values of this number for paths and cycles are
presented as well. The characterization result for a subset of the
vertex set of G to be a total global neighbourhood dominating set
for G is given and also characterized the graphs of order n(> 3)
having tgnd-numbers 2, n − 1, n.
