Strong incidence coloring of outerplanar graphs

An incidence in a graph G is a pair (v, e) where v is a vertex of G and e is an edge of G incident to v. Two incidences (v, e) and (u, f ) are adjacent if at least one of the following holds: (i) v = u, (ii) e = f, or (iii) edge vu = e or f. A strong incidence coloring of a graph G is a mapping from the set of incidences of G to the set of colors {1, ... , k} such that any two incidences that are adjacent or adjacent to the same incidence receive distinct colors. The minimum number of colors needed for a strong incidence coloring of a graph is called the strong incidence chromatic number. In this paper we prove that strong incidence chromatic number of every outerplanar graph G is at most 4 increment (G) and this bound is tight.& COPY; 2023 Elsevier B.V. All rights reserved.