On a Graph Connecting Hyperbinary Expansions
M. Brunetti, A. D'Aniello

TL;DR
This paper investigates the properties of a graph constructed from hyperbinary representations of integers, focusing on the conditions under which its fundamental group is abelian, revealing structural insights into these representations.
Contribution
It introduces a novel graph model for hyperbinary expansions and characterizes integers with abelian fundamental groups in this context.
Findings
Identifies integers with abelian fundamental groups in the hyperbinary expansion graph
Defines a new graph structure connecting hyperbinary representations
Provides structural properties of the graph A(n)
Abstract
Le n be any positive integer. A hyperbinary expansion of n is are presentation of n as sum of powers of 2, each power being used at most twice. In this paper we study some properties of a suitable edge-coloured and vertex-weighted oriented graph A(n) whose nodes are precisely the several hyperbinary representations of n. In particular, we identify those integers m in N such that the fundamental group of A(m) is abelian.
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Taxonomy
Topicsgraph theory and CDMA systems · Advanced Graph Theory Research · Graph Labeling and Dimension Problems
