Counting Coloured Graphs. III
- 1 February 1972
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 24 (1) , 82-89
- https://doi.org/10.4153/cjm-1972-010-7
Abstract
In an earlier paper [4], we found an asymptotic expansion for Mn = Mn(k), the number of coloured graphs on n labelled nodes, when n is large. Such a graph is a set of n distinguishable objects called nodes, and a set of “edges”, that is, undirected pairs of nodes. The nodes are mapped onto k colours. Every pair of nodes of different colours may or may not be joined by an edge, but no edge can join a pair of nodes of the same colour.We write mn for the number of these graphs which are connected, Fn for the number which use all k colours (i.e., at least one node in each graph is mapped onto each of the k colours), and fn for the number of connected graphs which use all k colours.Keywords
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