On Bandwidth and Cyclic Bandwidth of Graphs

Let \(B(G)\) and \(B_c(G)\) denote the bandwidth and cyclic bandwidth of graph \(G\), respectively. In this paper, we shall give a sufficient condition for graphs to have equal bandwidth and cyclic bandwidth. This condition is satisfied by trees. Thus all theorems on bandwidth of graphs apply to cyclic bandwidth of graphs satisfying the sufficiency condition, and in particular, to trees. We shall also give a lower bound of \(B_c(G)\) in terms of \(B(G)\).