The bandwidth sum of join and composition of graphs Original Research Article

Given a graph image, a proper labeling f of G is a one-to-one function image. The bandwidth sum of a graph G, denoted by image, is defined by image, where the minimum is taken for all proper labelings image of G. In this paper, we give some results for the bandwidth sum problem for the join of k graphs image, where each image is a path, cycle, complete graph, or union of isolated vertices. We also discuss the bandwidth sum for the composition of two graphs G and H, where G and H are path, cycle, or union of isolated vertices.