An eigenvalue characterization of antipodal distance-regular graphs
Summary: Let \(\Gamma\) be a regular (connected) graph with \(n\) vertices and \(d+1\) distinct eigenvalues. As a main result, it is shown that \(\Gamma\) is an \(r\)-antipodal distance-regular graph if and only if the distance graph \(\Gamma_d\) is constituted by disjoint copies of the complete graph \(K_r\), with \(r\) satisfying an expression in terms of \(n\) and the distinct eigenvalues.
scientific article; zbMATH DE number 1118014