2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78318The edge-bandwidth of a graph is the minimum, over all labelings of the edges with distinct integers, of the maximum difference between labels of two incident edges. We prove that edge-bandwidth is at least as large as bandwidth for every graph, with equality for certain caterpillars. We obtain sharp or nearly-sharp bounds on the change in edge-bandwidth under addition, subdivision, or contraction of edges. We compute edge-bandwidth for cliques, bicliques, caterpillars, and some theta graphs.12 pagesCombinatorics05C78, 05C35text