Riste Škrekovski: On 12-regular nut graphs; Some problems and results on some graph parameters

The seminar will consist of two talks:

Title: On 12-regular nut graphs

Speaker: Riste Škrekovski

Joint work with Nino Bašić and Martin Knor

Abstract: A nut graph is a simple graph whose adjacency matrix is singular with 1-dimensional kernel and corresponding eigenvector with no zero elements. For each d in {3,4,...,11} all values n for which there exists a d-regular nut graph of order n are known.

In the talk, we consider all values n for which there exists a 12-regular nut graph of order n.

Title: Some problems and results on some graph parameters

Speaker: Riste Škrekovski

Joint work with Aleksandra Tepeh and Martin Knor

Abstract: In the talk I will survey some open problems and results on Wiener index and several other related graph parameters.