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.

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