Geodesic
Genus distribution of graph amalgamations: Pasting when one root has arbitrary degree
Ars Mathematica Contemporanea, Tome 3 (2010) no. 2, pp. 121-138.

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This paper concerns counting the imbeddings of a graph in a surface. In the first installment of our current work, we showed how to calculate the genus distribution of an iterated amalgamation of copies of a graph whose genus distribution is already known and is further analyzed into a partitioned genus distribution (which is defined for a double-rooted graph). Our methods were restricted there to the case with two 2-valent roots. In this sequel we substantially extend the method in order to allow one of the two roots to have arbitrarily high valence.
DOI : 10.26493/1855-3974.111.e89
Keywords: Graph, genus distribution, vertex-amalgamation 
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Imran F. Khan; Mehvish I. Poshni; Jonathan L. Gross. Genus distribution of graph amalgamations: Pasting when one root has arbitrary degree. Ars Mathematica Contemporanea, Tome 3 (2010) no. 2, pp. 121-138. doi : 10.26493/1855-3974.111.e89. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.111.e89/

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