Pseudo-distance-regularised graphs are distance-regular or distance-biregular [article]

M. A. Fiol
2012 arXiv   pre-print
The concept of pseudo-distance-regularity around a vertex of a graph is a natural generalization, for non-regular graphs, of the standard distance-regularity around a vertex. In this note, we prove that a pseudo-distance-regular graph around each of its vertices is either distance-regular or distance-biregular. By using a combinatorial approach, the same conclusion was reached by Godsil and Shawe-Taylor for a distance-regular graph around each of its vertices. Thus, our proof, which is of an
more » ... ebraic nature, can also be seen as an alternative demonstration of Godsil and Shawe-Taylor's theorem.
arXiv:1205.5687v1 fatcat:m6aprsayjnachptw4m2svmmhzi