Domination topological indices and their polynomials of a firefly graph

Ahmed, Hanan; Salestina, M. Ruby; Alwardi, Anwar

doi:10.1080/09720529.2021.1882155

Cited by 6 publications

(6 citation statements)

References 12 publications

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“…Proof. From [23], DM 1 (G) = 4(r + s + 2), DM 2 (G) = 4(r + s + 1), and DM * 1 (G) = 4(r + s + 1). Therefore, by substitution of these values, the results are obtained.…”

Section: Definition 3 ([23]mentioning

confidence: 97%

Study on Structural Properties of Brain Networks Based on Independent Set Indices

Puthanpurakkal,

Ramachandran

2023

Symmetry

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Studies of brain network organisation have swiftly adopted graph theory-based quantitative analysis of complicated networks. Small-world topology, densely connected hubs, and modularity characterise the brain’s structural and functional systems. Many measures quantify graph topology. It has not yet been determined which measurements are most appropriate for brain network analysis. This work introduces a new parameter applicable to brain network analysis. This parameter may help in the identification of symmetry and the study of symmetry breakdown in the brain. This is important because decreased symmetry in the brain is associated with a decreased chance of developing neurodevelopmental and psychiatric disorders. This work is to study brain networks using maximal independent set-based topological indices. These indices seem to depict significant properties of brain networks, such as clustering, small-worldness, etc. One new parameter introduced in this paper for brain network analysis depends on Zagreb topological indices and independence degree. This parameter is useful for analyzing clusters, rich clubs, small-worldness, and connectivity in modules.

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“…Proof. From [23], DM 1 (G) = 4(r + s + 2), DM 2 (G) = 4(r + s + 1), and DM * 1 (G) = 4(r + s + 1). Therefore, by substitution of these values, the results are obtained.…”

Section: Definition 3 ([23]mentioning

confidence: 97%

Study on Structural Properties of Brain Networks Based on Independent Set Indices

Puthanpurakkal,

Ramachandran

2023

Symmetry

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“…Hanan Ahmed introduced the concept of domination topological indices in 2021 [31]. The domination topological index (DTI) is defined as the sum of the distances between each vertex and its nearest dominating vertex in a graph.…”

Section: Introductionmentioning

confidence: 99%

Symmetry-Adapted Domination Indices: The Enhanced Domination Sigma Index and Its Applications in QSPR Studies of Octane and Its Isomers

Wazzan

Ahmed

2023

Symmetry

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Molecular descriptors are essential in mathematical chemistry for studying quantitative structure–property relationships (QSPRs), and topological indices are a valuable source of information about molecular properties, such as size, cyclicity, branching degree, and symmetry. Graph theory has played a crucial role in the development of topological indices and dominating parameters for molecular descriptors. A molecule graph, under graph isomorphism conditions, represents an invariant number, and the graph theory approach considers dominating sets, which are subsets of the vertex set where every vertex outside the set is adjacent to at least one vertex inside the set. The dominating sigma index, a topological index that incorporates the mathematical principles of domination topological indices and the sigma index, is applicable to some families of graphs, such as book graphs and windmill graphs, and some graph operations, which have exact values for this new index. To evaluate the effectiveness of the domination sigma index in QSPR studies, a comparative analysis was conducted to establish an appropriate domination index that correlates with the physicochemical properties of octane and its isomers. Linear and non-linear models were developed using the QSPR approach to predict the properties of interest, and the results show that both the domination forgotten and domination first Zagreb indices exhibited satisfactory performance in comparison testing. Further research into QSAR/QSPR domination indices is required to build more robust models for predicting the physicochemical properties of organic compounds while maintaining the importance of symmetry.

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“…Most of the works on topological indices are extended to other fuzzy graphs like bipolar FGS, fuzzy incidence graphs and intuitionistic FGs. This work is inspired from the domination index on graphs defined by Ahmed et al [28]. In the article the domination degree of a vertex v is defined as the number of minimal dominating sets containing v. Motivated from this definition, this article discusses the domination degree and domination index in FGs using weight of strong arcs.…”

Section: Introductionmentioning

confidence: 99%

Strong incidence domination in fuzzy incidence graphs

Sunitha

2022

IFS

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Fuzzy Incidence graph (FIG) is one of the most suitable ways to model real life problems when there is an influence of the vertices on the edges. Domination in FIG is a novel concept which has many applications. The study aims to introduce a new concept of domination in fuzzy incidence graphs using strong pairs and define strong incidence domination number (SIDN) using weight of strong pairs. Minimal strong incidence dominating set (MSIDS) is defined and some of its properties are discussed. Bounds for the SIDN and the properties of strong incidence dominating sets (SIDS) of some FIGs are investigated. Also a social application of the SIDN is obtained.

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Domination topological indices and their polynomials of a firefly graph

Cited by 6 publications

References 12 publications

Study on Structural Properties of Brain Networks Based on Independent Set Indices

Study on Structural Properties of Brain Networks Based on Independent Set Indices

Symmetry-Adapted Domination Indices: The Enhanced Domination Sigma Index and Its Applications in QSPR Studies of Octane and Its Isomers

Strong incidence domination in fuzzy incidence graphs

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