Axiomatic characterization of the center function on fan graphs

Abstract

In graph theory, the center function identifies a set of vertices in a connected graph G that minimizes the maximum distance from any other vertex. We examine the behavior of the center function on connected graphs through a set of axioms. While universal axioms apply to all connected graphs, they cannot fully characterize certain graphs. To address this limitation, non-universal axioms for specific graph classes were introduced. This study is focused on establishing an axiomatic characterization of the center function on fan graphs by utilizing a combination of universal and non-universal axioms.