Estimation of most effected cycles and busiest network route based on complexity function of graph in fuzzy environment

Suppose ρ is a simple graph, then its eccentric harmonic index is defined as the sum of the terms 2 / e a + e b for the edges v a v b , where e a is the eccentricity of the a th vertex of the graph ρ . We symbolize the eccentric harmonic index (EHI) as H e = H e ρ . In this article, we determine H e for the Cartesian product (CP) of particularly chosen graphs. Lower bounds for H e of the CP of the two graphs are established. The formulas of EHI for the Hamming and Hypercube graphs are obtained. These obtained formulas can be used in QSAR and QSPR studies to get a better understanding of their applications in mathematical chemistry.

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“…Te harmonic index H(ρ) of a graph ρ was developed by the mathematician Fajtlowicz [5][6][7][8][9][10], and defned by…”

Section: Historical and Preliminary Overviewmentioning

confidence: 99%

“…Assume that the size of G□H � m. Ten, clearly m � n 1 m 2 + n 2 m 1 . Tus, by employing m, we can rewrite (8) as Ten,…”

Section: Corollary Supposementioning

confidence: 99%

Eccentric Harmonic Index for the Cartesian Product of Graphs

Jebreen

Aftab

Sowaity

et al. 2022

Journal of Mathematics

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“…In [9], the term complement of FGs was discussed. Poulik et al [10] shifted the term average connectivity from classical graphs to FGs. Overall, FGs have become useful in several fields, like networking, modelling, social sciences, the recognition of different patterns, etc.…”

Section: Introductionmentioning

confidence: 99%

Dominations in Intutionistic Fuzzy Directed Graphs with Applications towards Influential Graphs

Guan,

Khan,

Fida

et al. 2024

Mathematics

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In this manuscript, we introduce a few new types of dominations in intuitionistic fuzzy directed graphs (IFDGs) based on different types of strong arcs (SAs). Our work is not only a direct extension of domination in directed fuzzy graphs (DFGs) but also fills the gap that exists in the literature regarding the dominations in different extended forms of fuzzy graphs (FGs). In the beginning, we introduce several types of strong arcs in IFDGs, like semi-β strong arcs, semi-δ strong arcs, etc. Then, we introduce the concepts of domination in IFDGs based on these strong arcs and discuss its various useful characteristics. Moreover, the dominating set (DS), minimal dominating set (MDS), etc., are described with some fascinating results. We also introduce the concept of an independent set in IFDGs and investigate its relations with the DS, minimal independent set (MIS) and MDS. We also provide numerous important characterizations of domination in IFDGs based on minimal and maximal dominating sets. In this context, we discuss the lower and upper dominations of some IFDGs. In addition, we introduce the terms status and structurally equivalent and examine a few relationships with the dominations in IFDGs. Finally, we investigate the most expert (influential) person in the organization by utilizing the concepts of domination in IFGs.

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“…Practices prove that the coding method and iterative mode of the genetic algorithm are highly suitable for optimized solutions during test paper generation. In order to determine paper generation speed, the consuming time can be calculated on the basis of the complexity function [22]. Te standard indexes can be set and the quality of the paper generation system can be evaluated through the fuzzy graph theory [23].…”

Section: Introductionmentioning

confidence: 99%

Modelling and Simulation of Intelligent English Paper Generating Based on SSA‐GA

Li-min

Gao

Zhai

2023

Mathematical Problems in Engineering

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To enhance the quality and efficiency of computer-enabled generation of papers for Test for English Majors Band 8 (TEM-8), a paper generation model supported by sparrow search algorithm-genetic algorithm was studied. First, a simplified test paper generation mathematical model was set up after analyzing and studying types and characteristics of TEM-8 tasks. In the model, quantity, type, difficulty, discrimination degree, scores, exposure, and answering time of test questions were taken into consideration. To enhance the optimizing effect of the genetic algorithm for searching test questions, the traditional genetic algorithm was improved by introducing the sparrow search algorithm into the model to achieve a better crossover rate, variance rate, optimization precision, and speed of the genetic algorithm. A new sparrow search-genetic algorithm (SSA-GA) was designed, and the optimizing effect of SSA-GA was verified to be ideal through optimizing six standard test functions. Then, SSA-GA was applied to conduct experimentation with test paper generation, and comparison with traditional genetic algorithms was also made. The values of best and average fitness of SSA-GA were better than those of the traditional genetic algorithm (GA) in the paper generation. Exposure rate and success rate in TEM-8 paper generation of SSA-GA were higher than those of traditional GA in TEM-8 paper generation. Results showed that the studied SSA-GA could implement test paper generation with higher speed and better quality.

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Estimation of most effected cycles and busiest network route based on complexity function of graph in fuzzy environment

Cited by 21 publications

References 35 publications

Eccentric Harmonic Index for the Cartesian Product of Graphs

Eccentric Harmonic Index for the Cartesian Product of Graphs

Dominations in Intutionistic Fuzzy Directed Graphs with Applications towards Influential Graphs

Modelling and Simulation of Intelligent English Paper Generating Based on SSA‐GA

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