منابع مشابه
Integral trees with diameters 5 and 6
In this paper, some new families of integral trees with diameters 5 and 6 are constructed. All these classes are infinite. They are different from those in the existing literature. We also prove that the problem of finding integral trees of diameters 5 and 6 is equivalent to the problem of solving some Diophantine equations. The discovery of these integral trees is a new contribution to the sea...
متن کاملIntegral trees with diameters 4, 6 and 8
In this paper, some new families of integral trees with diameters 4, 6 and 8 are given. All these classes are infinite. They are different from those in the existing literature. We also prove that the problem of finding integral trees of diameters 4, 6 and 8 is equivalent to the problem of solving Pell’s diophantine equations. The discovery of these integral trees is a new contribution to the s...
متن کاملIntegral trees of odd diameters
A graph is called integral if all eigenvalues of its adjacency matrix consist entirely of integers. Recently, Csikvári proved the existence of integral trees of any even diameter. In the odd case, integral trees have been constructed with diameter at most 7. In this paper, we show that for every odd integer n > 1, there are infinitely many integral trees of diameter n. AMS Mathematics Subject C...
متن کاملSome new classes of integral trees with diameters 4 and 6
In this paper, some new classes of integral trees with diameters 4 and 6 are given. All these classes are infinite. They are different from those in the existing literature.
متن کاملIntegral Trees of Arbitrarily Large Diameters
In this paper we construct trees having only integer eigenvalues with arbitrarily large diameters. In fact, we prove that for every set S of positive integers there exists a tree whose positive eigenvalues are exactly the elements of S. If the set S is different from the set {1} then the constructed tree will have diameter 2|S|.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2005
ISSN: 0012-365X
DOI: 10.1016/j.disc.2005.04.007