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An infinite family of integral graphs

✍ Scribed by Moshe Roitman

Publisher: Elsevier Science
Year: 1984
Tongue: English
Weight: 272 KB
Volume: 52
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(84)90095-5

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✦ Synopsis

We obtain here an infinite family of integral complete tripartite grapbs. The 'purpose-of this note is to obtain an infinite family of integral mmpjete tripartite graphs. For background see [l]. We recall first some detitions and facts. A complete n-pu*te gnzph K(p*, l . l 5 p,,) is a graph with a set A = AI U l l l U A,, of p1 + = l l + p,, vertices, where & are nonempty disjoint sets, \Ai I= pi for 1s i G n, such that two vertices in A a~ adja;cent if and only if they belong to different Ai, Aj. A graph is caHed inaegm! if all the eigenvalues of its adjacency matrix are integers. The eigenvalues of a complete n-partite graph K(p,, _ . . , p,)) with p1 < p2 < l l

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