Abstract
Many graph‐colouring problems involve the colouring of the vertices or the edges of a graph in such a way that adjacent vertices or edges are differently coloured. During the 1980s there was increased interest in ‘total colourings’, in which both vertices and edges are coloured in such a way that adjacent vertices, adjacent edges, and incident vertices and edges, are differently coloured. In this paper, we investigate the total colouring of one particularly attractive class of graphs, the powers of paths.
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