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Algebra Seminar: Two Vertex Descriptors Based on Hosoya's Matching Descriptor Z(G).
2008-11-03
1:10 pm, Heill Hall 106W
Matt Hudelson
abstract: In 1971, Harao Hosoya launched the study of graph-theoretical descriptors in chemical applications by demonstrating a high correlation between the number of matchings of an alkane to its boiling point. We continue his legacy by describing two distinct vertex descriptors. The first of these descriptors is defined by æ(G,v)=Z(G)/Z(G-v) where Z(G) enumerates the n number of matchings, i.e. partitions of the vertex set into singletons and adjacent pairs, of the graph G. We will show that if G is a tree, then æ(G,v) can be approached via "tree expressions," a generalization of continued fractions. The second descriptor associates to each vertex in G a polynomial in á whose coefficients p_i (v) enumerate the n number of distinct paths of length i that begin at the vertex v. Together, adaptations of these descriptors form a "local vertex space" such that two vertices with similar local characteristics are mapped to points that are close in this space. As an application of such a space, we can quickly search large databases of chemical compounds for atoms with specific local connectivity environments.
Weekly Scheduled Seminars
For more information please contact the individuals listed below.Monday
1:10pmAlgebra Seminar - Google Group
Neill Hall 106W
Contact: Judi McDonald
Tuesday
4:30-5:30pmMathematics Education Seminar
One World Cafe - Moscow, ID
Contact: Libby Knott
Wednesday
3:00-4:00pmApplied Math Seminar
Neill Hall 3W
Contact: Alan Genz
4:00-5:00pm
Reliability and Risk Seminar
Neill Hall 106W
Contact: Haijun Li
Thursday
Friday
4:15-5:15pmSpatial Reasoning: An Interdisciplinary Seminar
Cleveland Annex 309
Contact Co-organizers: Kim Vincent and Kathleen Ryan, Interior Design.
Various disciplines dealing with spatial relationships and reasoning will be examined. We will discuss what spatial reasoning is and how to improve students' spatial reasoning. The book, Learning to Think Spatially: GIS as a Support System in the K-12 Curriculum will be used. A read-only version may be found at www.nap.edu/catalog.php?record_id=11019