Cyclic bandwidth with an edge added

Bc(G)Bc(G) denotes the cyclic bandwidth of graph G. In this paper, we obtain the maximum cyclic bandwidth of graphs of order p   with adding an edge e∈E[G¯] as follows:Bc(G+e)=2Bc(G)ifBc(G)⩽p8,13p2+2Bc(G)ifBc(G)>p8.We also show that this bound is sharp.