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Random Tensors$
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Răzvan Gheorghe Gurău

Print publication date: 2016

Print ISBN-13: 9780198787938

Published to Oxford Scholarship Online: January 2017

DOI: 10.1093/acprof:oso/9780198787938.001.0001

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The classification of edge colored graphs

The classification of edge colored graphs

Chapter:
(p.49) Chapter 4 The classification of edge colored graphs
Source:
Random Tensors
Author(s):

Razvan Gurau

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198787938.003.0004

This chapter presents the classification of the edge colored graphs by the degree. It is well known that the family of combinatorial maps of fixed genus is infinite and exponentially bounded. It turns out that the same holds for edge colored graphs, where the degree plays the role of the genus: the family of graphs of fixed degree is infinite and exponentially bounded. The graphs at fixed degree are enumerated explicitly, and the generating function of the family of graphs of fixed degree is computed.

Keywords:   enumeration of graphs, edge colored graphs, generating function

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