11 papers
Duality in Biperiodic Fibonacci Words Substitution Frequencies and Combinatorial Invariants
Jasem Hamoud
In this paper, a natural duality on the family of biperiodic Fibonacci words generated by the directive sequence . Both of $\mathfrak{F}^{(a…
On Epimorphisms of Hypergraphic Automata and Input Symbol Semigroups
Jasem Hamoud
Hypergraphic automata are automata whose state sets and output symbol sets are hypergraphs invariant under the actions of the transition and output functions. Universally attractin…
Sharp Bounds and Extremal Fuzzy Graphs for the Fuzzy Sombor Index
Jasem Hamoud
The fuzzy Sombor index applies the classical Sombor index to fuzzy graphs, incorporating both edge membership values and fuzzy vertex degrees. For , the general fuzzy Sombor i…
Theta-Relations Among Degree-Based Tree Indices
Duaa Abdullah, Jasem Hamoud
In this paper, degree-based topological indices play a key role in the structural analysis of graphs in this paper and have significant uses in chemical graph theory. We investigat…
Structural Components Dominate Asymptotic Behavior on Sombor Index with Iterated Pendant Constructions
Jasem Hamoud
The Sombor index, a degree-based topological descriptor introduced by Gutman in 2021, lacks closed-form expressions for complex hierarchical trees with multi-level pendant structur…
On Extremal Family Trees Beyond Caterpillars and Greedy Constructions
Jasem Hamoud, Duaa Abdullah
This paper investigates topological indices for the greedy tree associated with a graphic degree sequence $\mathscr{D} = (d_1 \geqslant d_2 \geqslant \dot…
Analysis of the Density of Words under Morphism
Jasem Hamoud, Duaa Abdullah
In this paper, we analyze the density of the Fibonacci word and its derived forms by examining the morphisms associated with each. It offers a comparative analysis of the density o…
Bounds on the Albertson Index for Trees with Given Degree Sequences
Jasem Hamoud, Duaa Abdullah
In this paper, we presents novel and sharp bounds on the Albertson index of trees, revealing deep connections between degree sequences and graph irregularity where the Albertson in…
On the Asymptotic Palindrome Density of Fibonacci Infinite Words
Duaa Abdullah, Jasem Hamoud
In this paper, we investigate the combinatorial and density properties of infinite words generated by Fibonacci-type morphisms, focusing on their subword structure, palindrome dens…
A Study of NP-Completeness and Undecidable Word Problems in Semigroups
Duaa Abdullah, Jasem Hamoud
In this paper we explore fundamental concepts in computational complexity theory and the boundaries of algorithmic decidability. We examine the relationship between complexity clas…
Extremal Degree Irregularity Bounds for Albertson and Sigma Indices in Trees and Bipartite Graphs
Jasem Hamoud, Duaa Abdullah
In this paper, the study of extreme value bounds for topological indices is crucial for understanding their influence on trees and bipartite graphs. For integers satisfying…