Regularity in Weighted Graphs a Symmetric Function Approach
Keywords:regular graphs, symmetric functions, D-finite, generating functions
AbstractThis 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.
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