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Integral trees with diameter four

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  • Wang, Ligong
  • Wang, Qi
  • Huo, Bofeng

Abstract

A graph is called integral if all eigenvalues of its adjacency matrix consist entirely of integers. In this paper, we investigate integral trees S(r;mi)=S(a1+a2+⋯+as;m1,m2,…,ms) of diameter 4 with s=3,4,5,6. Such integral trees are found by using a computer search or solving the Diophantine equations. New sufficient conditions for a construction of infinite families of integral trees S(r′;mi)=S(b1+⋯+bs;m1,…,ms) of diameter 4 from given integral trees S(r;mi)=S(a1+⋯+as;m1,…,ms) of diameter 4 are given. Further, using these conditions we construct infinitely many new classes of integral trees S(r′;mi)=S(b1+⋯+bs;m1,…,ms) of diameter 4 with s=3,4,5,6. Finally, we propose two basic open problems about integral trees of diameter 4 for further study.

Suggested Citation

  • Wang, Ligong & Wang, Qi & Huo, Bofeng, 2016. "Integral trees with diameter four," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 53-64.
    • Handle: RePEc:eee:apmaco:v:282:y:2016:i:c:p:53-64
    DOI: 10.1016/j.amc.2016.02.002
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    References listed on IDEAS

    as
    1. Shi, Yongtang, 2015. "Note on two generalizations of the Randić index," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 1019-1025.
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