Strong Chromatic Index of Outerplanar Graphs

The strong chromatic index χs′(G) of a graph G is the minimum number of colors needed in a proper edge-coloring so that every color class induces a matching in G. It was proved In 2013, that every outerplanar graph G with Δ≥3 has χs′(G)≤3Δ−3. In this paper, we give a characterization for an outerplanar graph G to have χs′(G)=3Δ−3. We also show that if G is a bipartite outerplanar graph, then χs′(G)≤2Δ; and χs′(G)=2Δ if and only if G contains a particular subgraph.