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To gain full voting privileges, let $p (n)$ be a path graph which has vertices $v (p)=\ {1,2,.,n\}$ in sequence Total domination in graphs was introduced by cockayne, dawes, and hedetniemi [18]and is now well studied in graph theory. What is the domination number of this graph

I pose some examples for myself and i realized that the domination number of a path graph with $n$ vertices is uprounding of $$\frac {n} {3}$$ Also we characterize the total domination number of the central graph of some families of graphs such as path graphs, cycle graphs, wheel graphs, complete graphs and com. Total dominating numbers are defined only for graphs having no isolated vertex (plus the trivial case of the singleton graph )

In other words, the total domination number is the size of a minimum total dominating set.

16.1.1 trees the upper total domination number of a path is established in [52] For n 2 an integer, γt( pn) 2 ( + )/3 n 1 = chellali, favaron, haynes, and raber [28] determined upper bounds on the upper total domination number of a tree Recall that the independence number α(

In this chapter we focus on the upper total domination number of a graph A set s of vertices in a graph g is a total dominating set in g if every vertex of g is adjacent to a vertex in s. Domination number of central graphs Indeed, we obtain some tight bounds for the total domination number of a central graph c(g) in te

Ms of some invariants of the graph g

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