Edge-Bandwidth of Graphs
Tao Jiang, Dhruv Mubayi, Aditya Shastri, Douglas B. West · SIAM Journal on Discrete Mathematics · 1999
The 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 K n , K n,n , caterpillars, and some theta graphs.