In this paper we consider the concept of preintersection numbers of a graph. These numbers are determined by the spectrum of the adjacency matrix of the graph, and generalize the intersection numbers of a distance-regular graph. By using the preintersection numbers we give some new spectral and quasi-spectral characterizations of distance-regularity, in particular for graphs with large girth or large odd-girth.
|Journal||Journal of Combinatorial Theory, Series A, Structures designs and application combinatorics|
|Publication status||Published - Oct 2016|
- distance-regular graph
- preintersection numbers