(2,1)-Total labelling of outerplanar graphs Original Research Article

The image-total labelling number image of a graph G is the width of the smallest range of integers that suffices to label the vertices and the edges of G such that no two adjacent vertices have the same label, no two adjacent edges have the same label and the difference between the labels of a vertex and its incident edges is at least 2. In this paper we prove that if G is an outerplanar graph with maximum degree image, then image if image, or image and G is 2-connected, or image and G contains no intersecting triangles.