We define a nearly platonic graph to be a finite k-regular simple planar graph in which all but a small number of the faces have the same degree. we show that it is impossible for such a graph to have exactly one disparate face, and offer some conjectures, including the conjecture that nearly platonic graphs with two disparate faces come in a small set of families.
|Original language||English (US)|
|Number of pages||18|
|Journal||Australasian Journal of Combinatorics|
|State||Published - Feb 2018|
Bibliographical notePublisher Copyright:
© 2018, University of Queensland. All rights reserved.