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Title: Colloquium: Complex adjacency spectra of (multi)digraphs
Speaker: Gopinath Sahoo (Bennett University, Noida)
Date: 18 November 2022
Time: 4 pm
Venue: Microsoft Teams (Online)

Given any graph, we can uniquely associate a square matrix which stores informations about its vertices and how they are interconnected. The goal of spectral graph theory is to see how the eigenvalues and eigenvectors of such a matrix representation of a graph are related to the graph structure. We consider here (multi)digraphs and define a new matrix representation for a multidigraph and named it as the complex adjacency matrix.

The relationship between the adjacency matrix and the complex adjacency matrix of a multidigraph are established. Furthermore, some of the advantages of the complex adjacency matrix over the adjacency matrix of a multidigraph are observed. Besides, some of the interesting spectral properties (with respect to the complex adjacency spectra) of a multidigraph are established. It is shown that not only the eigenvalues, but also the eigenvectors corresponding to the complex adjacency matrix of a multidigraph carry a lot of information about the structure of the multidigraph.

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 18 May 2024