Eigenvalues of the Laplacian on the Goldberg-Coxeter constructions for $3$- and $4$-valent graphs

Toshiaki Omori, Hisashi Naito, Tatsuya Tate

We are concerned with spectral problems of the Goldberg-Coxeter construction for $3$- and $4$-valent finite graphs. The Goldberg-Coxeter constructions ${\mathrm{GC}}_{k,l}(X)$ of a f…