Triangle path transit functions, betweenness and pseudo-modular graphs

The geodesic and induced path transit functions are the two well-studied interval functions in graphs. Two important transit functions related to the geodesic and induced path functions are the triangle path transit functions which consist of all vertices on all u , v -shortest (induced) paths or all vertices adjacent to two adjacent vertices on all u , v -shortest (induced) paths, for any two vertices u and v in a connected graph G . In this paper we study the two triangle path transit functions, namely the I Δ and J Δ on G . We discuss the betweenness axioms, for both triangle path transit functions. Also we present a characterization of pseudo-modular graphs using the transit function I Δ by forbidden subgraphs.