| | 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 $\mu$ as an eigenvalue of multiplicity
$k$. A {\em star set} for $\mu$ in $G$ is a set $X$ of $k$ vertices such that $\mu$ is not an eigenvalue of $G-X$. The induced subgraph $G-X$ is called a {\em star complement} for $\mu$ 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 $\mu \ne -1$ or $0$, and to determine all the graphs with spectra
in $[-2,\infty)$.
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 |
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