Integral Trees of Arbitrarily Large Diameters
نویسنده
چکیده
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|.
منابع مشابه
Integral 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 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 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 کاملGraph Polynomials and Graph Transformations in Algebraic Graph Theory
The thesis consists of two parts. In the first part we study two graph transformations,namely the Kelmans transformation and the generalized tree shift. In the second part of thisthesis we study an extremal graph theoretic problem and its relationship with algebraic graphtheory. The main results of this thesis are the following. • We show that the Kelmans transformation is a very ef...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009