Algebraic Graph Theory Seminar - Lavanya Selvaganesh

Title: Spectral Properties of the eccentricity matrix for special classes of graphs

Abstract:

Eccentricity matrix, another graph matrix, was originally proposed, as $D_{MAX}$ matrix, by Randi\'c in 2013 and redefined by Wang et al. in 2018 by using the concept of the eccentricities of vertices. In this talk, we will discuss the irreducibility and the spectral properties of the eccentricity matrix for special classes of graphs, such as trees, coalescence of complete graphs (windmill graphs), coalescence of cycles (Dutch windmill graphs).

In 2018, Wang et al. posed a conjecture which states that ``Among the trees on $n$ vertices, the tree with a vertex of degree $n-2$ has the minimum Ecc-spectral radius". We will also discuss the status of this conjecture.