| Description: | [DMS Seminar] Ranjit Mehatari (IISER Kolkata) -- Bounding normalized eigenvalues of Graphs |
| Date: | Thursday, Jun 30, 2016 |
| Time: | 2 p.m. - 3:30 p.m. |
| Venue: | 108, Lecture Hall Complex |
| Details: | Let $G$ be a simple, connected, undirected graph on $n$ vertices. The adjacency matrix $A$ of $G$ is $n\times n$ matrix with $a_{ij}=1$ when the vertices $i$ and $j$ are connected by an edge otherwise $a_{ij}=0$. The normalized adjacency $\cal{A}$ matrix is obtained by dividing each row of $A$ by corresponding row sum. The eigenvalues of $\cal{A}$ are called the normalized eigenvalues of $G$. It is easy to verify that 1 is always an simple eigenvalue of $\cal{A}$ and all other eigenvalues lie in the interval $[-1,0)$. We try to localize the eigenvalues of $\cal{A}$. We provide suitable bound for the eigenvalues other than 1 in terms of number of common neighbor between pair of vertices and their degrees. |
| Calendar: | Seminar Calendar (entered by anirban.banerjee) |