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{\bf Mehvish I. Poshni, Imran F. Khan and Jonathan L. Gross}
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{\bf Genus Distributions of 4-Regular Outerplanar Graphs}
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We present an $O(n^2)$-time algorithm for calculating the genus distribution of any 4-regular outerplanar graph. We characterize such graphs in terms of what we call \emph{split graphs} and \emph{incidence trees}. The algorithm uses post-order traversal of the incidence tree and \emph{productions} that are adapted from a previous paper that analyzes double-root \emph{vertex-amalgamations} and \emph{self-amalgamations}.

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