Adam Knudson

collaborators

2 papers

math.CO2023

Bounds on Kemeny's constant of a graph and the Nordhaus-Gaddum problem

Sooyeong Kim, Neal Madras, Ada Chan +3

We study Nordhaus-Gaddum problems for Kemeny's constant $K (G)$ of a connected graph $G$ . We prove bounds on $min {K (G), K (G)}$ and the pro…

math.CO2023

A Nordhaus-Gaddum type problem for the normalized Laplacian spectrum and graph Cheeger constant

J. Nolan Faught, Mark Kempton, Adam Knudson

For a graph $G$ on $n$ vertices with normalized Laplacian eigenvalues $0 = λ_{1} (G) \leq λ_{2} (G) \leq \dots \leq λ_{n} (G)$ and graph complement $G^{c}$ , we prove that \begin{equation*} \…