Joint ArizMATYC & Southwestern MAA Section Spring Meeting, Date: 2010/04/09 - 2010/04/10, Location: Scottsdale, AZ
Publication date:
2010-04-01
Proceedings of the Joint ArizMATYC & Southwestern MAA Section Spring Meeting
Author:
Kaatz, Forrest
Bultheel, Adhemar ; Podopivec, Andrej ; Estrada, Ernesto
Abstract:
We present new calculations for 2D tessellations including the topographical Wiener Index and statistical mechanics of graphs. We model ideal tilings, tilings from porous arrays, and random 2D graphs. The topological Wiener index is compared to the topographical index and we find for the porous array tilings that they are expanding in size as they progress outward. The adjacency matrix for the 2D graphs provides a means of calculating the Wiener Index and various statistical quantities such as entropy, free energy, partition function, and Helmholtz energy of the graphs.