More Maps of $p$-gons With a Ring of $q$-gons

Abstract

Deza and Grishukhin studied $3$-valent maps $M_n(p,q)$ consisting of a ring of $n$ $g$-gons whose inner and outer domains are filled by $p$-gons. They described the conditions for $n,p,q$ under which such a map may exist and presented several infinite families of them. We extend their results by presenting several new maps concerning mainly large values of $n$ and $q$.