We prove that the genus polynomials of the graphs called iterated claws are real-rooted. This continues our work directed toward the 25-year-old conjecture that the genus distribution of every graph is log-concave. We have previously established log-concavity for sequences of graphs constructed by iterative vertex-amalgamation or iterative edge-amalgamation of graphs that satisfy a commonly observable condition on their partitioned genus distributions, even though it had been proved previously that iterative amalgamation does not always preserve real-rootedness of the genus polynomial of the iterated graph. In this paper, the iterated topological operation is adding a claw, rather than vertex- or edge-amalgamation. Our analysis here illustrates some advantages of employing a matrix representation of the transposition of a set of productions.
@article{538,
title = {Iterated claws have real-rooted genus polynomials},
journal = {ARS MATHEMATICA CONTEMPORANEA},
volume = {11},
year = {2015},
doi = {10.26493/1855-3974.538.86e},
language = {EN},
url = {http://dml.mathdoc.fr/item/538}
}
Gross, Jonathan L.; Mansour, Toufik; Tucker, Thomas W.; Wang, David G. L. Iterated claws have real-rooted genus polynomials. ARS MATHEMATICA CONTEMPORANEA, Tome 11 (2015) . doi : 10.26493/1855-3974.538.86e. http://gdmltest.u-ga.fr/item/538/