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Three Classes of Bipartite Integral Graphs

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Discrete Geometry, Combinatorics and Graph Theory (CJCDGCGT 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4381))

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Abstract

A graph G is called integral if all zeros of its characteristic polynomial P(G, x) are integers. In this paper, the bipartite graphs K p, q(t), K p(s), q(t) and K p, q ≡ K q, r are defined. We shall derive their characteristic polynomials from matrix theory. We also obtain their sufficient and necessary conditions for the three classes of graphs to be integral. These results generalize some results of Balińska et al. The discovery of these integral graphs is a new contribution to the search of integral graphs.

Supported by NSFC (No.70571065) and DPOP in NPU.

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Authors and Affiliations

  1. Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, P.R. China

    Ligong Wang & Hao Sun

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  1. Ligong Wang
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  2. Hao Sun
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Jin Akiyama William Y. C. Chen Mikio Kano Xueliang Li Qinglin Yu

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Wang, L., Sun, H. (2007). Three Classes of Bipartite Integral Graphs. In: Akiyama, J., Chen, W.Y.C., Kano, M., Li, X., Yu, Q. (eds) Discrete Geometry, Combinatorics and Graph Theory. CJCDGCGT 2005. Lecture Notes in Computer Science, vol 4381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70666-3_22

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  • DOI: https://doi.org/10.1007/978-3-540-70666-3_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70665-6

  • Online ISBN: 978-3-540-70666-3

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