arXiv subjects

M. A. Fiol

Publications and source records attributed to M. A. Fiol.

74 records · Page 5Linked to original sources

arXiv2012

On some approaches to the spectral excess theorem for nonregular graphs

The Spectral Excess Theorem (SPET) for distance-regular graphs states that a regular (connected) graph is distance-regular if and only if its spectral-excess equals its average excess. Recently, some local or global approaches to the SPET have been used to obtain new versions of the theorem for nonregular graphs, and also to study the problem of characterizing the graphs which have the corresponding distance-regularity property. In this paper, some of these versions are related and compared, and some of their results are improved. As a result, a sufficient condition for a graph to be distance-polynomial is obtained.

math.SP↗

arXiv2012

Pseudo-distance-regularised graphs are distance-regular or distance-biregular

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.

math.CO↗