Grundy Total Hop Dominating Sequences in Graphs

Let G = (V(G), E(G)) be an undirected graph with gamma(C) not equal 1 for each component C of G. Let S = (v(1), v(2), center dot center dot center dot, v(k)) be a sequence of distint vertices of a graph G, and let (S) over cap = {v(1), v(2), . . . , v(k)}. Then S is a legal open hop neighborhood sequence if N-G(2)(v(i)) \ boolean OR(i-1)(j=1) N-G(2)(v(j)) not equal circle divide for every i is an element of{2, . . . , k}. If, in addition, (S) over cap is a total hop dominating set of G, then S is a Grundy total hop dominating sequence. The maximum length of a Grundy total hop dominating sequence in a graph G, denoted by gamma(th)(gr)(G), is the Grundy total hop domination number of G. In this paper, we show that the Grundy total hop domination number of a graph G is between the total hop domination number and twice the Grundy hop domination number of G. Moreover, determine values or bounds of the Grundy total hop domination number of some graphs.