2012/05/25 by M.A. Fiol, M. A. Fiol, Fiol, M. A. · 1 citation
Computer Science · Mathematics · #05C50 #05E30 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #math.CO #msc:05C50 #msc:05E30
paper · pdf · doi:10.48550/arxiv.1205.5687
arxiv created 2012/05/25 · openalex publication_date 2012/05/25 · arxiv updated 2012/05/28 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/04
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 algebraic nature, can also be seen as an alternative demonstration of Godsil and Shawe-Taylor's theorem.