Genus distribution of graph amalgamations: Pasting when one root has arbitrary degree

Imran F. Khan, Mehvish I. Poshni, Jonathan L. Gross
2010 Ars Mathematica Contemporanea  
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
more » ... thod in order to allow one of the two roots to have arbitrarily high valence.
doi:10.26493/1855-3974.111.e89 fatcat:sq7qh4h53jej5mr7itz6x2tsai