Eigenvalues and Equations of the Laplacian

Tables of Eigenvalues

Since the Octagasket (OG) does not belong to Kigami's family of PCF fractals there is no nice formula relating consecutive graph energies. In view of this we define the unnormalized discrete Laplacian as,

where Ave(u(y)) denotes the average value of u on the 2 or 4 neighboring points.

From this we expect,