A theorem for an axiomatic approach to metric properties of graphs
Ladislav Nebeský · Czechoslovak Mathematical Journal · 2000
By a graph we mean here a finite undirected graph without loops and multiple edges (i.e. a graph in the sense of [2], for example).Studying graphs we will investigate sets of ordered triples of vertices.For the sake of brevity, the ordered triple (u, v, x) of any objects u, v and x will be denoted by uvx.Let G be a connected graph, and let d G denote its distance function.Obviously, the vertex set V (G) of G together with d G create a metric space.Following [6], by a step in G we mean an ordered triple uvx ∈ (V (G)) 3 such that * Research supported by the Grant Agency of the Czech Republic, grant No. 405/95/1554.