Bounds in radial Moore graphs of diameter 3
Jesús M. Ceresuela, Nacho López · Discrete Mathematics · 2025
Radial Moore graphs preserve the order and the regularity of Moore graphs and allow some vertices to have more eccentricity than they should have in a Moore graph. One way to classify their resemblance with a Moore graph is the status measure. The status of a graph is defined as the sum of the distances of all pairs of ordered vertices and equals twice the Wiener index. Vertices with minimum eccentricity are called central vertices. In this paper we study upper bounds for both the maximum number of central vertices and the status of radial Moore graphs. Finally, we present a family of radial Moore graphs of diameter 3 that is conjectured to have maximum status.