We derive a recursion for the genus distributions of the graphs obtained by iteratively attaching a claw to the dipole $D_3$. The minimum genus of the graphs in this sequence grows arbitrarily large. The families of graphs whose genus distributions have been calculated previously are either planar or almost planar, or they can be obtained by iterative single-vertex or single-edge amalgamation of small graphs. A significant simplifying construction within this calculation achieves the effect of an amalgamation at three vertices with a single root vertex, rather than with multiple roots.
@article{10_37236_2278,
author = {Jonathan L. Gross and Imran F. Khan and Mehvish I. Poshni},
title = {Genus distributions for iterated claws},
journal = {The electronic journal of combinatorics},
year = {2014},
volume = {21},
number = {1},
doi = {10.37236/2278},
zbl = {1300.05078},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2278/}
}
TY - JOUR
AU - Jonathan L. Gross
AU - Imran F. Khan
AU - Mehvish I. Poshni
TI - Genus distributions for iterated claws
JO - The electronic journal of combinatorics
PY - 2014
VL - 21
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/2278/
DO - 10.37236/2278
ID - 10_37236_2278
ER -
%0 Journal Article
%A Jonathan L. Gross
%A Imran F. Khan
%A Mehvish I. Poshni
%T Genus distributions for iterated claws
%J The electronic journal of combinatorics
%D 2014
%V 21
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/2278/
%R 10.37236/2278
%F 10_37236_2278
Jonathan L. Gross; Imran F. Khan; Mehvish I. Poshni. Genus distributions for iterated claws. The electronic journal of combinatorics, Tome 21 (2014) no. 1. doi: 10.37236/2278
