Geodesic
Genus distributions of graphs under self-edge-amalgamations
Ars Mathematica Contemporanea, Tome 5 (2012) no. 1, pp. 127-148.

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We investigate the well-known problem of counting graph imbeddings on all oriented surfaces with a focus on graphs that are obtained by pasting together two root-edges of another base graph. We require that the partitioned genus distribution of the base graph with respect to these root-edges be known and that both root-edges have two 2-valent endpoints. We derive general formulas for calculating the genus distributions of graphs that can be obtained either by self-co-amalgamating or by self-contra-amalgamating a base graph whose partitioned genus distribution is already known. We see how these general formulas provide a unified approach to calculating genus distributions of many new graph families, such as co-pasted and contra-pasted closed chains of copies of the triangular prism graph, as well as graph families like circular and Möbius ladders with previously known solutions to the genus distribution problem.
DOI : 10.26493/1855-3974.166.63e
Keywords: Graph, genus distribution, edge-amalgamation 
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Mehvish I. Poshni; Imran F. Khan; Jonathan L. Gross. Genus distributions of graphs under self-edge-amalgamations. Ars Mathematica Contemporanea, Tome 5 (2012) no. 1, pp. 127-148. doi : 10.26493/1855-3974.166.63e. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.166.63e/

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