The edge-bandwidth of theta graphs

An edge-labeling f of a graph G is an injection from E(G) to the set of int egers. The edge-bandwidth of G is B'(G) = min(f){B'(f)}, where B'(f) is the maximum difference between labels of incident edges of G. The theta graph Theta(l(1),,...,l(m)) is the graph consisting of m pairwise internally disj oint paths with common endpoints and lengths l(1)less than or equal to...le ss than or equal to l(m). We determine the edge-bandwidth of all theta grap hs. (C) 2000 John Wiley & Sons,