On Colourings of Wheel Graph (Wn)

Graph colourings and partitions

In this paper we have investigated mainly the three colouring parameters of a graph G, viz., the chromatic number, the achromatic number and the pseudoachromatic number. The importance of their study in connection with the computational complexity, partitions, algebra, projective plane geometry and analysis were brie.y surveyed. Some new results were found along these directions. We have rede0n...

On conjectures on the defining set of (vertex) graph colourings

Connectedness of the graph of vertex-colourings

For a positive integer k and a graph G, the k-colour graph of G, Ck(G), is the graph that has the proper k-vertex-colourings of G as its vertex set, and two k-colourings are joined by an edge in Ck(G) if they differ in colour on just one vertex of G. In this note some results on the connectivity of Ck(G) are proved. In particular it is shown that if G has chromatic number k ∈ {2, 3}, then Ck(G)...

Anagram-free colourings of graph subdivisions

An anagram is a word of the form WP where W is a non-empty word and P is a permutation of W . A vertex colouring of a graph is anagram-free if no subpath of the graph is an anagram. Anagram-free graph colouring was independently introduced by Kamčev, Łuczak and Sudakov and ourselves. In this paper we introduce the study of anagram-free colourings of graph subdivisions. We show that every graph ...

Loops, regular permutation sets and graph colourings

We establish a correspondence among loops, regular permutation sets and directed graphs with a suitable edge colouring and relate some algebraic properties of the loop to configurations of the associated graph.