Integral complete multipartite graphs

Ligong Wang, Xiaodong Liu

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14 引用 (Scopus)

摘要

A graph is called integral if all eigenvalues of its adjacency matrix are integers. In this paper, we investigate integral complete r-partite graphs Kp1, p2, ..., pr = Ka1 · p1, a2 · p2, ..., as · ps with s = 3, 4. We can construct infinite many new classes of such integral graphs by solving some certain Diophantine equations. These results are different from those in the existing literature. For s = 4, we give a positive answer to a question of Wang et al. [Integral complete r-partite graphs, Discrete Math. 283 (2004) 231-241]. The problem of the existence of integral complete multipartite graphs Ka1 · p1, a2 · p2, ..., as · ps with arbitrarily large number s remains open.

源语言英语
页(从-至)3860-3870
页数11
期刊Discrete Mathematics
308
17
DOI
出版状态已出版 - 6 9月 2008

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