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.
@article{166,
title = {Genus distributions of graphs under self-edge-amalgamations},
journal = {ARS MATHEMATICA CONTEMPORANEA},
volume = {4},
year = {2011},
doi = {10.26493/1855-3974.166.63e},
language = {EN},
url = {http://dml.mathdoc.fr/item/166}
}
Poshni, Mehvish I.; Khan, Imran F.; Gross, Jonathan L. Genus distributions of graphs under self-edge-amalgamations. ARS MATHEMATICA CONTEMPORANEA, Tome 4 (2011) . doi : 10.26493/1855-3974.166.63e. http://gdmltest.u-ga.fr/item/166/