Total and paired domination numbers of $$C_m$$ bundles over a cycle $$C_n$$Cn

Let (G=(V,E)) be a simple graph without isolated vertices. A set (S) of vertices is a total dominating set of a graph (G) if every vertex of (G) is adjacent to some vertex in (S). A paired dominating set of (G) is a dominating set whose induced subgraph has a perfect matching. The minimum cardinality of a total dominating set (respectively, a paired dominating set) is the total domination number (respectively, the paired domination number). Hu and Xu (J Combin Optim 27(2):369–378, 2014) computed the exact values of total and paired domination numbers of Cartesian product (C_nsquare C_m) for (m=3,4). Graph bundles generalize the notions of covering graphs and Cartesian products. In this paper, we generalize these results given in Hu and Xu (J Combin Optim 27(2):369–378, 2014) to graph bundle and compute the total domination number and the paired domination number of (C_m) bundles over a cycle (C_n) for (m=3,4). Moreover, we give the exact value for the total domination number of Cartesian product (C_nsquare C_5) and some upper bounds of (C_m) bundles over a cycle (C_n) where (mge 5).