On distance preserving and sequentially distance preserving graphsSmith, Jason P. (Avtor) Zahedi, Emad (Avtor) distance preservingisometric subgraphsequentially distance preservingchordalcut vertexsimplicial vertexA graph H is an isometric subgraph of G if d_H(u,v)=d_G(u,v), for every pair u,v ∈ V(H). A graph is distance preserving if it has an isometric subgraph of every possible order. A graph is sequentially distance preserving if its vertices can be ordered such that deleting the first i vertices results in an isometric subgraph, for all i≥1. We give an equivalent condition to sequentially distance preserving based upon simplicial orderings. Using this condition, we prove that if a graph does not contain any induced cycles of length 5 or greater, then it is sequentially distance preserving and thus distance preserving. Next we consider the distance preserving property on graphs with a cut vertex. Finally, we define a family of non-distance preserving graphs constructed from cycles.Založba Univerze na Primorskem20252025-11-03 11:34:48Članek v reviji22068sl