A NOTE ON THE EQUISEPARABLE TREES
نویسندگان
چکیده مقاله:
Let T be a tree and n_{l}(eIT) and n_{2}(eIT) denote the number of vertices of T, lying on the two sides of the edge e. Suppose T_{l} and T_{2} are two trees with equal number of vertices, e in T_{1} and f in T_{2}. The edges e and f are said to be equiseparable if either n_{l}(eIT_{I}) = n_{l}(fIT_{2}) or n_{l}(eIT_{I}) = n_{2}(fIT_{2}). If there is an one-to-one correspondence between the vertices of T_{l} and T_{2} such that the corresponding edges are equisep arable, then T_{ }and T_{2} are called equiseparable trees. Recently, Gutman, Arsic and Furtula investigated some equiseparable alkanes and obtained some useful rules (see J. Serb. Chem. Soc. (68)7 (2003), 549-555). In this paper, we use a combinatorial argument to find an equivalent def inition for equiseparability and then prove some results about relation of equiseparability and isomorphism of trees. We also obtain an exact expression for the number of distinct alkanes on n vertices which three of them has degree one.
منابع مشابه
A Note on Search Trees
Proof. Proceed by contradiction. Suppose that f has more than one root in (0,∞). Let r1 and r2, with r1 < r2, be two consecutive such roots (note that we can always find two consecutive roots r1 and r2 because f (r) > 0 for any root r). From the hypothesis, we have f (r1) > 0 and f (r2) > 0. Since f ′ is continuous at r1, there exists an 0 < 2 < (r2− r1) such that f (x) > 0 in the interval (r1,...
متن کاملDetermination of Large Families and Diameter of Equiseparable Trees
We consider the problem of determining all the members of an arbitrary family of equiseparable trees. We introduce the concept of saturation (based on the number partitions). After that, we use the same concept to obtain the least upper bound for the difference in the diameters of two equiseparable trees with m edges. We prove that this bound is equal to (m−4)/3, where m is the size of trees.
متن کاملA Note on the Integrity of Trees
We amend some results in the literature. We verify a formula for the integrity of the binomial tree, and correct formulas for the integrity of the complete k-ary tree. Dedicated to Henda Swart with the greatest thanks.
متن کاملA Note on Optical Routing on Trees
Bandwidth is a very valuable resource in wavelength division multiplexed optical networks. The problem of nding an optimal assignment of wavelengths to requests is of fundamental importance in bandwidth utilization. We present a polynomial-time algorithm for this problem on xed constant-size topologies. We combine this algorithm with ideas from Raghavan and Upfal 15] to obtain an optimal assign...
متن کاملA Note on Community Trees in Networks
We introduce the concept of community trees that summarizes topological structures within a network. A community tree is a tree structure representing clique communities from the clique percolation method (CPM). The community tree also generates a persistent diagram. Community trees and persistent diagrams reveal topological structures of the underlying networks and can be used as visualization...
متن کاملA Note on Completely Disconnecting Trees
Ginsburg and Sands defined a procedure for completely disconnecting graphs: each round, remove at most one edge from each component and at most w edges total. Define fw(g) to be the minimal number of rounds to reduce G to isolated vertices. Prior work of Ginsburg and Sands has determined fw(Pn) for 2 ≤ w ≤ ∞ and the lead-term asymptotics of f∞(Kn) and f2(Kn)). We show that when T is a tree with...
متن کاملمنابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ذخیره در منابع من قبلا به منابع من ذحیره شده{@ msg_add @}
عنوان ژورنال
دوره 2 شماره None
صفحات 15- 20
تاریخ انتشار 2007-05
با دنبال کردن یک ژورنال هنگامی که شماره جدید این ژورنال منتشر می شود به شما از طریق ایمیل اطلاع داده می شود.
میزبانی شده توسط پلتفرم ابری doprax.com
copyright © 2015-2023