77 citations · 956 across the 77 of their papers we have counts for
5 papers · 1 filter
Mean distance on metric graphs
Luís N. Baptista, James B. Kennedy, Delio Mugnolo
We introduce a natural notion of mean (or average) distance in the context of compact metric graphs, and study its relation to geometric properties of the graph. We show that it ex…
What is actually a metric graph?
Delio Mugnolo
Metric graphs are often introduced based on combinatorics, upon "associating" each edge of a graph with an interval; or else, casually "gluing" a collection of intervals at their e…
The Cheeger constant of a quantum graph
James B. Kennedy, Delio Mugnolo
We review the theory of Cheeger constants for graphs and quantum graphs and their present and envisaged applications.
General Cheeger inequalities for p-Laplacians on graphs
Matthias Keller, Delio Mugnolo
We prove Cheeger inequalities for p-Laplacians on finite and infinite weighted graphs. Unlike in previous works, we do not impose boundedness of the vertex degree, nor do we restri…
Parabolic theory of the discrete p-Laplace operator
Delio Mugnolo
We study the discrete version of the -Laplacian. Based on its variational properties we discuss some features of the associated parabolic problem. Our approach allows us in turn…