Integral complete multipartite graphs
نویسندگان
چکیده
A graph is called integral if all eigenvalues of its adjacency matrix are integers. In this paper, we investigate integral complete r-partite graphsKp1,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. © 2007 Elsevier B.V. All rights reserved. MSC: 05C50; 11D04; 11D72
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 308 شماره
صفحات -
تاریخ انتشار 2008