Total and paired domination numbers of $$C_m$$ bundles over a cycle $$C_n$$Cn |
| |
Authors: | Fu-Tao Hu Moo Young Sohn Xue-gang Chen |
| |
Institution: | 1.School of Mathematical Sciences,Anhui University,Hefei,China;2.Department of Mathematics,Changwon National University,Changwon,Korea;3.Department of Mathematics,North China Electric Power University,Beijing,China |
| |
Abstract: | 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 \(C_n\square C_m\) 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 \(C_n\square C_5\) and some upper bounds of \(C_m\) bundles over a cycle \(C_n\) where \(m\ge 5\). |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|