Bandwidth of the corona of two graphs

The bandwidth B(G) of a graph G is the minimum of the quantity max{|f(u)-f(v)|:uv∈E(G)} taken over all injective integer numberings f of G. The corona of two graphs G and H, written as G°H, is the graph obtained by taking one copy of G and |V(G)| copies of H, and then joining the ith vertex of G to every vertex in the ith copy of H. In this paper, we investigate the bandwidth of the corona of two graphs. For a graph G, we denote the connectivity of G by κ(G). Let G be a graph on n vertices with B(G)=κ(G)=k?2 and let H be a graph of order m. Let c,p and q be three integers satisfying 1?c?k-1 and . We define h_i=(2k-1)m+(k-i)(⌊(2k-1)m/i⌋+1)+1 for i=1,2,…,k and b=max{⌈(n(m+1)-qm-1)/(p+2)⌉,⌈(n(m+1)+k-q-1)/(p+3)⌉}. Then, among other results, we prove that