Geodesic
Genus distributions of 4-regular outerplanar graphs
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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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 split graphs and incidence trees. The algorithm uses post-order traversal of the incidence tree and productions that are adapted from a previous paper that analyzes double-root vertex-amalgamations and self-amalgamations.
DOI : 10.37236/699
Classification : 05C10, 05C05
Mots-clés : split graphs, incidence trees 
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     author = {Mehvish I. Poshni and Imran F. Khan and Jonathan L. Gross},
     title = {Genus distributions of 4-regular outerplanar graphs},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/699},
     zbl = {1230.05113},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/699/}
}
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Mehvish I. Poshni; Imran F. Khan; Jonathan L. Gross. Genus distributions of 4-regular outerplanar graphs. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/699

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