Regularity in Weighted Graphs a Symmetric Function Approach

Keywords: regular graphs, symmetric functions, D-finite, generating functions

Abstract

This work describes how the class of k-regular multigraphs with edge multiplicities from a finite set can be expressed using symmetric species results of Mendez. Consequently, the generating functions can be computed systematically using the scalar product of symmetric functions. This gives conditions on when the classes are D-finite using criteria of Gessel, and a potential route to asymptotic enumeration formulas.

Author Biography

Marni Mishna, Simon Fraser University
Dept. Mathematics Associate Professor

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Published
2018-12-31
Section
Articles