News & Events

Fouzul Atik

Monday, September 14, 2020 - 15:30 to 16:30
SMS Conference Room (via GoogleMeet)
Fouzul Atik
SRM University
On equitable partition of matrices and some problems related to graph theory

A partition of a square matrix A is said to be equitable if all the block of the partitioned matrix have constant row sums and each of the diagonal block is of square order. A quotient matrix Q of a square matrix A corresponding to an equitable partition is a matrix whose entries are the constat row sums of the corresponding blocks of A. A quotient matrix is an useful tool to find some eigenvalues of the matrix A. I will discuss some matrices whose eigenvalues are the eigenvalues of A and which are not the eigenvalues of a quotient matrix. Using this result we find eigenvalue localization theorems for matrices having an equitable partition. Finally, I will discuss some problems related to distance regular graph, Gersgorin disk theorem and distance matrix of graphs.

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