Characterization of the center function on Barbell graphs and (m,n)–lollipops using universal axioms

Source abstract

Let [Formula: see text] be any set of vertices in a graph [Formula: see text]. The center function outputs the set of all vertices that minimizes the maximum distance to the vertices in [Formula: see text]. The axiomatic characterization of the center function identifies consensus axioms that define its properties. An axiom becomes universal for the center function if it holds for all connected graphs. This paper aims to characterize axiomatically the center function on two subclasses of block graphs, namely, Barbell graphs and [Formula: see text]-lollipops.