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Operations Research Transactions ›› 2011, Vol. 15 ›› Issue (2): 19-27.

• Original Articles • Previous Articles     Next Articles

Some New Families of Integral Trees of Diameter Four

 WANG  Li-Gong,   Zhang-Zheng   

  • Online:2011-06-15 Published:2011-06-15
  • Supported by:

    Supported by the  National Natural Science Foundation of China　(No. 10871158),  the Natural Science Foundation of Shaanxi　Province (No. SJ08A01) and  the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.

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Abstract: An integral graph is a graph of which all the eigenvalues of its　adjacency matrix are integers. This paper investigates itegral trees of diameter 4.　Many new classes of such integral trees are cnstructed ifinitely by solving some　certain Diophantine equations. These results generalize some results of Wang, Li
and Zhang (see Families of integral trees with diameters 4, 6 and 8, Discrete Applied　Mathematics, 2004, 136: 349-362).

Key words: Operations research, integral tree, chracteristic polynomial, diophntine equation, graph spectrum

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