Strongly regular fusions of tensor products of strongly regular graphs
Let \(G\) and \(H\) be strongly regular graphs with (0, 1)-adjacency matrices \(A_ 0= I\), \(A_ 1\), \(A_ 2= J-I- A_ 1\) and \(B_ 0= I\), \(B_ 1,\) \(B_ 2= J- I- B_ 1\) respectively. The tensor product \(G\otimes H\) is defined to be the nine class association scheme with adjacency matrices \(A_ i\otimes B_ j\). By combining (fusing) some of these nine classes, it is sometimes possible to obtain a third strongly regular graph \(F\). The main result of this paper is a complete classification of all parameter sets for strongly regular graphs \(G\), \(H\) and \(F\) for which such a fusion is possible.
scientific article; zbMATH DE number 645230
scientific article