An algorithm to check the equality of total domination number and double of domination number in graphs

In graph theory, domination number and its variants such as total domination number are studied by many authors. Let the domination number and the total domination number of a graph G without isolated vertices be gamma(G) and gamma(t)(G), respectively. Based on the inequality gamma(t)(G) <= 2 gamma(G), we investigate the graphs satisfying the upper bound, that is, graphs G with gamma(t)(G) = 2 gamma(G). In this paper, we present some new properties of such graphs and provide an algorithm which can determine whether gamma(t)(G) = 2 gamma(G) or not for a family of graphs not covered by the previous results in the literature.