Total and paired domination numbers and γ-total and γ-paired dominating graphs of some graphs

Let G be a graph without isolated vertices. A total dominating set of G is a set D ⊆ V(G) such that every vertex of G is adjacent to at least one vertex in D. A paired dominating set of G is a total dominating set whose induced subgraph contains a perfect matching. The total (paired) domination number of G is the minimum cardinality of a total (paired) dominating set of G. The γ-total (γ-paired) dominating graph of G is the graph whose vertex set contains all minimum total (paired) dominating sets of G, and two vertices of this graph are adjacent if they differ by exactly one vertex. In this dissertation, we determine the total domination numbers and the paired domination numbers of some cylinders, some wheel related graphs, windmill graphs, lollipop graphs, umbrella graphs, and coconut graphs. We also determine the γ-total dominating graphs and the γ-paired dominating graphs of some families of graphs including some graphs mentioned above.