Comment on “Wiener index of a fuzzy graph and application to illegal immigration networks”

Islam, Sk Rabiul; Maity, Sayantan; Pal, Madhumangal

doi:10.1016/j.fss.2019.08.006

Cited by 14 publications

(7 citation statements)

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“…Such authors investigated their research in domination set of class of graph concepts such as metric dimension, domination set, edge-identification chain and ring can be developed in the concept of dominating sets in the paper (10,11) . This research investigates the prevailing of acyclic graphs and binomial graphs metric dimension of Corona product graphs (12)(13)(14) . The symmetric difference network, minimal spanning tree algorithm, labelled vertices, and congruent dominating graph can be used to compute the seidel energy (15,16) .…”

Section: Introductionmentioning

confidence: 99%

Some Standard Seidel Energy Results of the Minimum Maximal Dominating Graphs

Manthiram,

Annamalai

2024

IJST

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Objectives: Let be a finite and connected graph with β points and d edges. In this research, introduced the graph's minimum maximal dominating seidel energy ( and the properties of the latent roots of the given parameters are discussed. Method: In this research, the seidel energy of several graphs and its properties are investigated. Examined its minimum maximal limits and computed a few conventional seidel energy outcomes for the minimum maximal dominating graphs. Finding: Using the minimum maximal dominating seidel energy of graphs, significant outcomes were achieved for complete graphs, complete bipartite graphs, and star graphs. The properties of the class of graphs were computed. The established upper and lower bound is . Novelty: The seidel energy of the proposed research findings is used in various graphs based on the research. The fundamental characteristics of a graph, such as its energy upper and lower bounds, have been determined, and this knowledge has found notable chemical applications in the conjugated molecular orbital theory. Recommendations for future energy-related research are presented and examined. Keywords: Connected graph, Dominating set, Latent roots, Minimum maximal, Seidel energy

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Section: Introductionmentioning

confidence: 99%

Some Standard Seidel Energy Results of the Minimum Maximal Dominating Graphs

Manthiram,

Annamalai

2024

IJST

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“…Islam et al [26] explored first Zegrab index and used it in a multi-criteria decision making (MCDM) to determine the best employee in a company. The Wiener index for fuzzy graphs are defined in [14,25]. The authors establish the relation between fuzzy Wiener index and fuzzy connectivity index.…”

Section: Introductionmentioning

confidence: 99%

“…The authors establish the relation between fuzzy Wiener index and fuzzy connectivity index. Islam et al [25] used fuzzy Wiener index in problem of illegal immigration network. Dinar et al [16] studied the Wiener index for an intuitionistic fuzzy graph.…”

Section: Introductionmentioning

confidence: 99%

Wiener Energies of Fuzzy Graphs with Application in Total Quality Management

Ahmad

Hussain

Saeid

2023

Preprint

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In this paper, fuzzy Wiener matrix, Wiener Laplacian matrix and corresponding energies of fuzzy graph are defined. A bound on largest eigenvalue of fuzzy Wiener matrix is presented. Several results related to eigenvalues of fuzzy Wiener and fuzzy Wiener Laplacian matrices are proved. Several upper and lower bounds for energies of these matrices are also established in terms of parameters like, number of vertices, edges, minimum and maximum vertex and edge membership, etc. Finally, the idea of fuzzy Wiener energy is applied in multi criteria decision making of best organizations based on implementation of total quality management(TQM) attributes.

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“…In the beginning Wiener [29] discover the Wiener index (WI) when examining the heat capacity of paraffin. Binu et al [12] investigated the distance based index which is WI in FGs and application to illegal migration routes. Islam and Pal [15] recently stated the fuzzy hyper Wiener index (FHWI), along with certain limitations on the FHWI for various FGs such as path, cycle, and star.…”

Section: Introductionmentioning

confidence: 99%

Connectivity index of directed rough fuzzy graphs and its application in traffic flow network

Ahmad

Nawaz

2023

Granul. Comput.

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The directed rough fuzzy graph (DRFG) is a fusion of rough and fuzzy theory, because it deals with incomplete and vague information simultaneously. Connection or the strength of connectivity (SC) is vital in the realm of circuits or networks that are linked to the real world. As a result, SC is one of the most essential aspects of a directed rough fuzzy network system. The neighborhood connectivity index (N CI) is one such parameter that has a variety of applications in network theory. In this paper, we discuss the notion of N CI in DRFGs using the strength of vertices to their neighbor vertices. We provide several lower and upper bounds on the N CI of DRFGs with reference to other graph invariants such as the number of vertices, edges, and degree distance. When we study N CI in operations for DRFGs with a large number of vertices, the degree of vertices in a DRFG provides a confusing picture. Therefore, a mechanism to determine the N CI for DRFG operations is needed. Therefore, generalized formulas for N CI of DRFGs obtained by operations such as union, composition, and Cartesian product are also developed. An algorithm for obtaining N CI of DRFGs is also proposed. In addition, an application of N CI of DRFGs in traffic flow networks was discussed to identify the busiest intersection using the proposed algorithm. Finally, we gave a complete comparative evaluation and analysis table for a similar human trafficking system, comparing the results for connectivity index (CI), Wiener index (WI), and N CI.

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Comment on “Wiener index of a fuzzy graph and application to illegal immigration networks”

Cited by 14 publications

References 1 publication

Some Standard Seidel Energy Results of the Minimum Maximal Dominating Graphs

Some Standard Seidel Energy Results of the Minimum Maximal Dominating Graphs

Wiener Energies of Fuzzy Graphs with Application in Total Quality Management

Connectivity index of directed rough fuzzy graphs and its application in traffic flow network

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