Isotemporal classes of n-gons
| dc.creator | de Bivort, Benjamin | |
| dc.date | 2005-01-11 | |
| dc.date.accessioned | 2026-07-07T05:15:59Z | |
| dc.date.available | 2026-07-07T05:15:59Z | |
| dc.description | Here I present the present the first major result of a novel form of network analysis - a temporal interpretation. Treating numerical edges labels as the time at which an interaction occurs between the two vertices comprising that edge generates a number of intriguing questions. For example, given the structure of a graph, how many ``fundamentally'' different temporally non-isomorphic forms are there, across all possible edge labelings. Specifically, two networks, N and M, are considered to be in the same isotemporal class if there exists a function alpha(N)->M that is a graph isomorphism and preserves all paths in N with strictly increasing edge labels. I present a closed formula for the number of isotemporal classes N(n) of n-gons. This result is strongly tied to number theoretic identities; in the case of $n$ odd, N(n)= 1/n sum_{d|n} (2^{n/d -1}-1)Phi(d), where Phi is the Euler totient function. | |
| dc.description | 28 pages, 5 figures | |
| dc.identifier | https://arxiv.org/abs/math/0501171 | |
| dc.identifier | http://arxiv.org/abs/math/0501171 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73824 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 05C60 (primary) 05C78 (secondary) | |
| dc.title | Isotemporal classes of n-gons | |
| dc.type | text |