Some New Families of Integral Trees of Diameter Four

An integral graph is a graph of which all the eigenvalues of its adjacency matrix are integers. This paper investigates integral trees of diameter 4. Many new classes of such integral trees are constructed infinitely 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). Keywords Operations research, integral tree, characteristic polynomial, dio- phantine equation, graph spectrum Subject Classification (GB/T 13745-1992) 110.74