School of Mathematics  April 8, 2008 


 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 $GX$. The induced subgraph $GX$ 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  14:0016:00
Wednsday, April 16, 2008  14:0015:00
 
Place: Lecture Hall, Niavaran Bldg., Niavaran Sqr., Tehran, Iran 