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School of Mathematics - April 8, 2008 |
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| | Peter Rowlinson
University of Stirling
Stirling, Scotland
April 14 & 16, 2008
First talk:
Star Complements in Finite Graphs (April 14) |
ABSTRACT: Let G be a graph with μ as an eigenvalue of multiplicity
k. A {\em star set} for μ in G is a set X of k vertices such that μ is not an eigenvalue of G−X. The induced subgraph G−X is called a {\em star complement} for μ in G. Star sets and star complements exist for any eigenvalue of any graph. They can be used to characterize graphs, to find sharp upper bounds for k when μ≠−1 or 0, and to determine all the graphs with spectra
in [−2,∞). |
Second talk:
Uses of the Adjacency Matrix (April 16)
ABSTRACT: We show how eigenvalues and eigenvectors of a (0,1) adjacency
matrix can be used to establish structural properties of finite graphs.
Illustrations include the Friendship Theorem, regular edge decompositions of a complete graph, and a characterization of harmonic graphs. |
Information |
| Time and Date: |
Monday, April 14, 2008 - 14:00-16:00
Wednsday, April 16, 2008 - 14:00-15:00
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| Place: Lecture Hall, Niavaran Bldg., Niavaran Sqr., Tehran, Iran |
