3 papers
math.CO2026
The Music and Mathematics of Maximal Evenness in Graphs
Neal Bushaw, Brent Cody, Luke Freeman +1
We use the concept of electric potential energy from physics, the mathematical field of graph theory, and the notion of majorization to study maximal evenness in a broader mathemat…
math.CO2025
The Wiener index of vertex colorings
Viktoriya Bardenova, Neal Bushaw, Brent Cody +2
The Wiener index of a vertex coloring of a graph is defined to be the sum of all pairwise geodesic distances between vertices of the same color. We provide characterizations of ver…
math.CO2025
Sets of vertices with extremal energy
Neal Bushaw, Brent Cody, Chris Leffler
We define various notions of energy of a set of vertices in a graph, which generalize two of the most widely studied graphical indices: the Wiener index and the Harary index. We pr…