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Density Characterization with The Upper Bound of Density of Fibonacci Word
Duaa Abdullah, Jasem Hamoud
This paper investigates the natural density and structural relationships within Fibonacci words, the density of a Fibonacci word is where deno…
Closed-Form Analysis and Extremal Bounds of Albertson and Sigma Indices in Trees with Prescribed Degree Sequences
Jasem Hamoud, Alexey Belov Yakovlevich, Muaadh Almahalebi +1
This study explores the irregularity properties of trees with prescribed degree sequences by analyzing two prominent topological indices: the Albertson index and the sigma index. W…
Optimal Behaviour in Extremal Bounds for -Irregularity
Jasem Hamoud, Duaa Abdullah
In this paper, we establishe the extremal bounds of the topological indices -- Sigma index -- focusing on analyzing the sharp upper bounds and the lower bounds of the Sigma index,…
Extremal Bounds on the Sigma and Albertson Indices for Non-Decreasing Degree Sequences
Jasem Hamoud, Duaa Abdullah
We establish sharp extremal bounds on the Albertson and Sigma irregularity indices for trees with prescribed degree sequences, with emphasis on caterpillar trees as key extremal co…
Bounds of Trees with Degree Sequence-Based Topological Indices on Specialized Graph Classes
Jasem Hamoud, Duaa Abdullah
In this paper, the investigates Adriatic indices, specifically the sum lordeg index where it defined as and the variable sum ex…
The Density of Zero and One in Fibonacci Word for Subwords and Their Palindromes
Duaa Abdullah, Jasem Hamoud
This paper studies the density of zero and one in subwords of the Fibonacci word with lengths less than thirty and compares them to the densities of their corresponding palindromes…
Applications of Combinatorics on Words with Symbolic Dynamics
Duaa Abdullah, Jasmem Hamoud
In this paper, we explore applications of combinatorics on words across various domains, including data compression, error detection, cryptographic protocols, and pseudorandom numb…
On Topological Indices in Trees: Fibonacci Degree Sequences and Bounds
Jasem Hamoud, Alexei Belov-Kanel, Duaa Abdullah
In this paper, we have studied bounds based on topological indicators, from which we selected Albertson index and the Sigma index . The Sigma index was defined th…
Bounds on Trees with Topological Indices Among Degree Sequence
Jasem Hamoud, Alexei Belov-Kanel, Duaa Abdullah
In this paper, we investigate The relationship between the Albertson index and the first Zagreb index for trees. For a tree with vertices and edges, we pr…
Novel Constructions of Words with Strong Avoidance Properties and their Combinatorial Analysis
Duaa Abdullah, Jasem Hamoud
This paper begins with a comprehensive overview of combinatorics on words and symbolic dynamics, covering their historical origins, fundamental concepts, and interconnections. Buil…
Topological Indices Among Strong Support Vertex
Jasem Hamoud, Duaa Abdullah
In this paper, we provide the irregularity properties of trees with strong support vertex by analyzing two prominent topological indices: the Albertson index and the Sigma index. W…
Irregularity and Topological Indices in Fibonacci Word Trees and Modified Fibonacci Word Index
Jasem Hamoud, Duaa Abdullah
This paper introduces the concept of the Fibonacci Word Index , a novel topological index derived from the Albertson index, applied to trees constructed from Fi…
Generalized Natural Density $\DF(\mathfrak{F}_n)$ of Fibonacci Word
Jasem Hamoud, Duaa Abdullah
This paper explores profound generalizations of the Fibonacci sequence, delving into random Fibonacci sequences, -Fibonacci words, and their combinatorial properties. We establi…
Improvement Ergodic Theory For The Infinite Word on Fibonacci Density
Jasem Hamoud, Duaa Abdullah
The paper explores combinatorial properties of Fibonacci words and their generalizations within the framework of combinatorics on words. These infinite sequences, measures the dive…
Dynamic and Programmatic Analysis of Fibonacci Word Density
Duaa Abdullah, Jasem Hamoud
Fibonacci word is the archetype of the Sturmian word, and it is one of the most studied of combinatorics on words. We studied the properties of the Fibonacci word and found its den…
Topological Indices With Degree Sequence of Tree
Jasem Hamoud, Duaa Abdullah
In this paper, we refer to a asymptotic degree sequence as . The examination of topological indices on trees gives us a general overview through bo…
Regularities of Typical Sigma Index on Caterpillar Trees of Pendent Vertices
Jasem Hamoud, Duaa Abdullah
In this paper, topological indices play a significant role in the analysis of caterpillar trees, especially due to their applications in chemical graph theory. We presented a study…