# 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.