## Highly regular graphs.(English)Zbl 0792.05093

Capobianco, Michael F. (ed.) et al., Graph theory and its applications: East and West. Proceedings of the first China-USA international conference, held in Jinan, China, June 9-20, 1986. New York: New York Academy of Sciences,. Ann. N. Y. Acad. Sci. 576, 20-29 (1989).
A graph $$G$$ of order $$p \geq 3$$ is highly regular if there exists an $$n \times n$$ matrix $$C=[c_{ij}]$$, where $$2 \leq n<p$$, called a collapsed adjacency matrix (CAM), such that for each vertex $$v$$ of $$G$$ there is a partition of $$V(G)$$ into $$n$$ subsets $$V_ 1=\{v\}$$, $$V_ 2,\dots,V_ n$$, such that each vertex $$y \in V_ j$$ is adjacent to $$c_{ij}$$ vertices in $$V_ i$$. In this article we develop some of the properties of highly regular graphs.
For the entire collection see [Zbl 0788.00046].

### MSC:

 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.) 05C99 Graph theory