The Fibonacci tree is a rooted binary tree whose number of vertices admit a recursive definition similar to the Fibonacci numbers. In this paper, we prove that a hypercube of dimensionhadmits two edge-disjoint Fibonacci trees of heighth, two edge-disjoint Fibonacci trees of heighth-2, two edge-disjoint Fibonacci trees of heighth-4and so on, as subgraphs. The result shows that an algorithm with Fibonacci trees as underlying data structure can be implemented concurrently on a hypercube network with no communication latency.

Lakshmanan K

Department of Analytics

School of Computer Science and Engineering

Vellore Campus

Raman I

Fulltext

Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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Edge-Disjoint Fibonacci Trees in Hypercube

Journal of Computer Networks and Communications

We give a new representation of the Fibonacci numbers. This is achieved using Fibonacci trees. With the help of this representation, the nth Fibonacci number can be calculated without having any knowledge about the previous Fibonacci numbers.

ISRN Discrete Mathematics

A Note on Closed-Form Representation of Fibonacci Numbers Using Fibonacci Trees

Discrete Applied Mathematics

Tricyclic graph with maximal Estrada index

Filomat

On the Harary index of cacti

A height balanced tree is a rooted binary tree T in which for every vertex v ∈ V(T), the difference bT (v) between the heights of the subtrees, rooted at the left and right child of v is at most one. We show that a height-balanced tree Th of height h is a subtree of the hypercube Qh+1 of dimension h + 1, if Th contains a path P from its root to a leaf such that bTh(v) = 1, for every non-leaf vertex v in P. A Fibonacci tree Fh is a height balanced tree Th of height h in which bFh(v) = 1, for every non-leaf vertex. F h has f(h + 2) - 1 vertices where f(h + 2) denotes the (h + 2)th Fibonacci number. Since f(h) ∼ 20.694h, it follows that if F h is a subtree of Qn, then n is at least 0.694(h+2). We prove that Fh is a subtree of the hypercube of dimension approximately 0.75h. © 2008 Korean Society for Computational and Applied Mathematics.

Journal of Applied Mathematics and Computing

Embedding height balanced trees and Fibonacci trees in hypercubes

Discrete Mathematics

On median nature and enumerative properties of Fibonacci-like cubes

Journal	Journal of Computer Networks and Communications
Publisher	Hindawi Limited
ISSN	2090-7141
Open Access	Yes