Total global neighbourhood domination

A subset D of the vertex set of a connected graph G is called a total global neighbourhood dominating set(tgnd-set) of C if and only if 1) is a total dominating sot of G as well as G(N), where G(N) 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 gamma(tgn)(G). In this paper sharp bounds for gamma(tgn) 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 Mid also characterized the graphs of order n(>= 3) having tgad-numbers 2, n - 1, n.