Abstract
Abstract We discuss the relationship between the structure of a graph and the spectrum of its adjacency matrix, and we describe a classic application of linear algebra to distance-regular graphs. The notions of graph angles and star partitions enable us to explore the influence on graph structure of an individual eigenvalue. The representation of a finite graph by a matrix provides an immediate link between linear algebra and graph theory. If the vertices of the graph G are labelled 1, 2, … , n, then the corresponding adjacency matrix A is the n × n matrix whose ij-entry is 1 if the vertices i and j are adjacent, and 0 if they are non-adjacent. Thus A is a symmetric matrix with zero diagonal; see Fig. 6.1 for a simple example.
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