# Seminar: Cyclic base orderings and uniformly dense networks

Seminar in Discrete Mathematics

**Speaker**: Rachel K. Gouveia

**Title**: Cyclic base orderings and uniformly dense networks

**Time**: Friday November 13, 1pm, Lippitt 205

**Abstract**: One of the principle areas of interest in graph theory is analysis of networks and their strengths.

Our research looks at a proposed method of determining which networks are uniformly dense.

A graph is a collection of points called vertices and lines called edges connecting some pairs of vertices.

A cycle occurs in a graph when its edges form a closed loop. A cyclic ordering of the edges of a graph is

any way to list all the edges such that the first follows the last. For a network modeled as a graph G, we

define a quantity h(G) as the largest number of consecutive edges in an ordering where the edges do not

form a cycle. Kajitani conjectures in Discrete Math., 72 (1988), 187 – 194 that a connected network G

is uniformly dense if and only if h(G) = n-1, where n is the number of nodes in G. Our research places bounds

on h(G) for a few infinite classes of graphs. Joint work with Jonathan D. Ashbrock and Hong-Jian Lai.

See http://www.math.uri.edu/~thoma/dmg/dmg.html

for further information and updates.