Counting Coloured Graphs

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Abstract
A graph on n labelled nodes is a set of n objects called “nodes”, distinguishable from each other, and a set (possibly empty) of “edges,” that is, pairs of nodes. Each edge is said to join its pair of nodes, at most one edge joins any two nodes and no edge joins a node to itself. By a k-colouring of such a graph we mean a mapping of the nodes of the graph onto a set of k distinct colours, such that no two nodes joined by an edge are mapped onto the same colour. We take k > 1.

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