Discrete Mathematics Group at URI

Discrete Mathematics Seminar

Spring 2021

April 16 E. Barranca, URI Integral Cographs (MS Presentation)

Abstract: Graphs whose eigenvalues are all integers are called integral graphs. It has been shown that out of 164,059,830,476 connected graphs on 12 vertices, only 325 of them are integral. In this presentation, we will explore a family of integral graphs: the cographs with balanced cotrees. Working with an algorithm which diagonalizes the adjacency matrix of a cograph, we will find closed forms for the eigenvalues of these cographs with balanced cotrees, showing they are integers. Lastly, we will show how to use these results on the spectrum of cographs with balanced cotrees to estimate the eigenvalues for any cograph.

Fall 2020

April 16	E. Barranca, URI	Integral Cographs (MS Presentation)
		Abstract: Graphs whose eigenvalues are all integers are called integral graphs. It has been shown that out of 164,059,830,476 connected graphs on 12 vertices, only 325 of them are integral. In this presentation, we will explore a family of integral graphs: the cographs with balanced cotrees. Working with an algorithm which diagonalizes the adjacency matrix of a cograph, we will find closed forms for the eigenvalues of these cographs with balanced cotrees, showing they are integers. Lastly, we will show how to use these results on the spectrum of cographs with balanced cotrees to estimate the eigenvalues for any cograph.