Regularity in Weighted Graphs: A Symmetric Function Approach
arXiv:1507.05121
Abstract
In this note we consider -regular multigraphs, where the possible edge multiplicities are controlled. These structures are considered in a question recently posed by Brendan McKay. We express the generating functions using the scalar product of symmetric functions, and consequently give conditions on when the classes are D-finite. We appeal to symmetric species results of Mendez to write the expressions in a systematic way.
9 pages