The edge-bandwidth of theta graphs
Dennis Eichhorn, Dhruv Mubayi, Kevin O’Bryant, Douglas B. West · Journal of Graph Theory · 2000
An edge-labeling f of a graph G is an injection from E(G) to the set of integers. The edge-bandwidth of G is B′(G) = minf {B′(f)} where B′(f) is the maximum difference between labels of incident edges of G. The theta graph Θ(l1,…,lm) is the graph consisting of m pairwise internally disjoint paths with common endpoints and lengths l1 ≤ ··· ≤ lm. We determine the edge-bandwidth of all theta graphs. © 2000 John Wiley & Sons, Inc. J Graph Theory 35: 89–98, 2000