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The contents of this report are the sole responsibility of the authors. O conteúdo do presente relatório é de única responsabilidade dos autores. Abstract The total chromatic number χ T (G) is the least number of colours needed to colour the vertices and edges of a graph G, such that no incident or adjacent elements (vertices or edges) receive the same(More)
An ordered pair (π, cπ) is said to be a gap-[k]-edge-labelling (gap-[k]vertex-labelling) if π is an edge-labelling (vertex-labelling) on the set {1, . . . , k}, and cπ is a proper vertex-colouring induced by a gap-function based on π. Gap-[k]edge-labellings and gap-[k]-vertex-labellings were first introduced by M. Tahraoui et al. [7] and A. Dehghan et al.(More)