An infinite family of integral graphs (Q761469)

The author constructs an infinite family of complete tripartite graphs all of whose eigenvalues are integers. These graphs are denoted \(K(p_ 1,p_ 2,p_ 3)\) with \(p_ 1=4u^ 2(u^ 2+v^ 2)^ 3,\) \(p_ 2=4v^ 2(u^ 2+v^ 2)^ 3,\) \(p_ 3=3u^ 2v^ 2(34u^ 2v^ 2-u^ 4-v^ 4)\) where u and v are positive integers with \((3-\sqrt{8})v<u<v.\) He remarks that other infinite families of integral complete n-partite graphs probably exist with \(n>3\). Indeed, there are probably other infinite families with \(n=3\).