Pseudo-distance-regularized graphs are distance-regular or distance-biregular
| Autor: | Miguel Angel Fiol |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
Discrete mathematics
Numerical Analysis Algebra and Number Theory Distance-biregular graph Symmetric graph Neighbourhood (graph theory) Local spectrum Distance-regular graph Geometric graph theory Planar graph Combinatorics symbols.namesake Vertex-transitive graph Graph power Predistance polynomials symbols Discrete Mathematics and Combinatorics Regular graph Geometry and Topology 05C50 Pseudo-distance-regular graph 05E30 Mathematics |
| Zdroj: | Linear Algebra and its Applications. 437:2973-2977 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2012.07.019 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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