On quadratic orbital networks

Abstract

These are some informal remarks on quadratic orbital networks over finite fields. We discuss connectivity, Euler characteristic, number of cliques, planarity, diameter and inductive dimension. We find a non-trivial disconnected graph for d=3. We prove that for d=1 generators, the Euler characteristic is always non-negative and for d=2 and large enough p the Euler characteristic is negative. While for d=1, all networks are planar, we suspect that for d larger or equal to 2 and large enough prime p, all networks are non-planar. As a consequence on bounds for the number of complete sub graphs of a fixed dimension, the inductive dimension of all these networks goes 1 as p goes to infinity.

13 figures 15 pages

References in corpus (3)

• The McKean-Singer Formula in Graph Theory
• Natural orbital networks
• Dynamically generated Networks

Cited by in corpus (3)

• Classical mathematical structures within topological graph theory
• The amazing world of simplicial complexes
• Characteristic Length and Clustering