### Symmetric Bipartite Graphs and Graphs with Loops

*Grant Cairns, Stacey Mendan*

#### Abstract

We show that if the two parts of a finite bipartite graph have the
same degree sequence, then there is a bipartite graph, with the same
degree sequences, which is symmetric, in that it has an involutive
graph automorphism that interchanges its two parts. To prove this,
we study the relationship between symmetric bipartite graphs and
graphs with loops.

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