Regular Article
Enumeration of Labelled (k, m)-Trees

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Abstract

Ak-graph is called a (k, m)-tree if it can be obtained from a single edge by consecutively adding edges so that every new edge containskmnew vertices while its remainingmvertices are covered by an already existing edge. We prove that there are(e(km)+m)!(e(km)−e+1)e−2e!m!((km)!)edistinct vertex labelled (k, m)-trees witheedges.

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Communicated by the Managing Editors

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Supported by an External Research Studentship, Trinity College, Cambridge, UK.

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