### On families of 2-nearly Platonic graphs

#### Abstract

*k*|

*d*) is a

*k*-regular planar graph with

*f*faces,

*f*− 2 of which are of size

*d*and the remaining two are of sizes

*d*

_{1},

*d*

_{2}, both different from

*d*. Such a graph is called balanced if

*d*

_{1}=

*d*

_{2}. We show that all connected 2-nearly Platonic graphs are necessarily balanced. This proves a recent conjecture by Keith, Froncek, and Kreher.

#### Keywords

#### Full Text:

PDFDOI: http://dx.doi.org/10.5614/ejgta.2022.10.2.23

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