Modular Decomposition of Graphs and the Distance Preserving Property

Emad Zahedi, Jason P. Smith

Research output: Contribution to journalArticlepeer-review

7 Downloads (Pure)


Given a graph G, a subgraph H is isometric if dH (u,v) = dG (u,v) for every pair u,v €, V (H), where d  is the distance function. A graph G  is distance preserving (dp) if it has an isometric subgraph of every possible order. A graph is sequentially distance preserving (sdp) if its vertices can be ordered such that deleting the first i  vertices results in an isometric subgraph, for all i ≥ 1 . We introduce a generalisation of the lexicographic product of graphs, which can be used to non-trivially describe graphs. This generalisation is the inverse of the modular decomposition of graphs, which divides the graph into disjoint clusters called modules. Using these operations, we give a necessary and sufficient condition for graphs to be dp. Finally, we show that the Cartesian product of a dp graph and an sdp graph is dp.
Original languageEnglish
Pages (from-to)192-198
Number of pages7
JournalDiscrete Applied Mathematics
Early online date16 May 2019
Publication statusPublished - 31 Jul 2019


  • Distance peserving
  • Isometric
  • Modular decoposition
  • Lexicographic product
  • Cartesian product


Dive into the research topics of 'Modular Decomposition of Graphs and the Distance Preserving Property'. Together they form a unique fingerprint.

Cite this