Integral trees with diameters 5 and 6
نویسندگان
چکیده
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 search for such trees.
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 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 کاملA survey of results on integral trees and integral graphs
A graph G is called integral if all zeros of the characteristic polynomial P (G, x) are integers. Our purpose is to determine or to characterize which graphs are integral. This problem was posed by Harary and Schwenk in 1974. In general, the problem of characterizing integral graphs seems to be very difficult. Thus, it makes sense to restrict our investigations to some interesting families of g...
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 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
عنوان ژورنال:
- Discrete Mathematics
دوره 297 شماره
صفحات -
تاریخ انتشار 2005