منابع مشابه
The minimal number with a given number of divisors
A number n is said to be ordinary if the smallest number with exactly n divisors is p q1−1 1 · · · p qa−1 a where q1 · · · qa is the prime factorization of n and q1 ≥ . . . ≥ qa (and where pk denotes the k-th prime). We show here that all square–free numbers are ordinary and that the set of ordinary numbers has natural density one.
متن کاملOn minimal energies of trees with given diameter
The energy of G, denoted by E(G), is defined as the sum of the absolute values of the eigenvalues of G. In this paper, the trees with a given diameter having the minimal energy are determined by three specific tree operations; using this method, together with previous work, a conjecture proposed by B. Zhou and F. Li [J. Math. Chem., 39:465–473, 2006] is completely solved.
متن کاملEla on Minimal Energies of Trees with given Diameter∗
The energy of G, denoted by E(G), is defined as the sum of the absolute values of the eigenvalues of G. In this paper, the trees with a given diameter having the minimal energy are determined by three specific tree operations; using this method, together with previous work, a conjecture proposed by B. Zhou and F. Li [J. Math. Chem., 39:465–473, 2006] is completely solved.
متن کاملOn the minimal energy of trees with a given diameter
The energy of a graph is defined as the sum of the absolute values of all eigenvalues of the graph. Zhang et al (Discrete Appl. Math., 92(1999), 71-84) characterized the trees with a perfect matching having the minimal and the second minimal energies, which solved a conjecture proposed by Gutman (J. Math. Chem., 1(1987), 123-143). In this letter, for a given positive integer d we characterize t...
متن کاملThe Number of Subtrees of Trees with Given Degree Sequence
This article investigates some properties of the number of subtrees of a tree with given degree sequence. These results are used to characterize trees with the given degree sequence that have the largest number of subtrees, which generalize the recent results of Kirk and Wang (SIAM J Discrete Math 22 (2008), 985–995). These trees coincide with those which were proven by Wang and independently Z...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1987
ISSN: 0012-365X
DOI: 10.1016/0012-365x(87)90131-2