A new fuzzy graph parameter for the comparison of human trafficking chains

Sebastian, Arya; Mathew, Sunil; Mordeson, John N.

doi:10.1016/j.fss.2022.04.016

Cited by 4 publications

(1 citation statement)

References 29 publications

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“…Recently, Sreenanda et al [12] investigated a comprehensive study on perpect fuzzy graphs, including the relationship between the chromatic numbers of a fuzzy graph and its complement graph, and the relationship between the perfection of a fuzzy graph and its underlying crisp graph. The readers may refer to [13][14][15] for more detail in the research on fuzzy graphs.…”

Section: Introductionmentioning

confidence: 99%

Adjacent Vertex Distinguishing Coloring of Fuzzy Graphs

Gong

Zhang

2023

Mathematics

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In this paper, we consider the adjacent vertex distinguishing proper edge coloring (for short, AVDPEC) and the adjacent vertex distinguishing total coloring (for short, AVDTC) of a fuzzy graph. Firstly, this paper describes the development process, the application areas, and the existing review research of fuzzy graphs and adjacent vertex distinguishing coloring of crisp graphs. Secondly, we briefly introduce the coloring theory of crisp graphs and the related theoretical basis of fuzzy graphs, and add some new classes of fuzzy graphs. Then, based on the α-cuts of fuzzy graphs and distance functions, we give two definitions of the AVDPEC of fuzzy graphs, respectively. A lower bound on the chromatic number of the AVDPEC of a fuzzy graph is obtained. With examples, we show that some results of the AVDPEC of a crisp graph do not carry over to our set up; the adjacent vertex distinguishing chromatic number of the fuzzy graph is different from the general chromatic number of a fuzzy graph. We also give a simple algorithm to construct a (d,f)-extended AVDPEC for fuzzy graphs. After that, in a similar way, two definitions of the AVDTC of fuzzy graphs are discussed. Finally, the future research directions of distinguishing coloring of fuzzy graphs are given.

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Section: Introductionmentioning

confidence: 99%

Adjacent Vertex Distinguishing Coloring of Fuzzy Graphs

Gong

Zhang

2023

Mathematics

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A fuzzy planar subgraph formation model for partitioning very large-scale integration networks

Kalathian,

Ramalingam,

Deivanayagampillai

2023

Decision Analytics Journal

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Solution of road network problem with the help of m-polar fuzzy graph using isometric and antipodal concept

Mondal

Mahapatra

Xin

et al. 2023

Sci Rep

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The isometry in crisp graph theory is a well-known fact. But, isometry under a fuzzy environment was developed recently and studied many facts. In a m-polar fuzzy graph, we have to think m components for each node and edge. Since, in our consideration, we consider m components for each nodes as well as edges, therefore we can not handle this type of situation using fuzzy model as their is a single components for this concept. Again, we can not apply bipolar or intuitionistic fuzzy graph model as each edges or nodes have just two components. Thus, these mPFG models give more efficient fuzziness results than other fuzzy model. Also, it is very interesting to develop and analyze such types of mPFGs with examples and related theorems. Considering all those things together, we have presented isometry under a m-polar fuzzy environment. In this paper, we have discussed the isometric m-polar fuzzy graph along with many exciting facts about it. Metric space properties have also been implemented on m-polar fuzzy isometric graph. We also have initiated a generalized fuzzy graph, namely antipodal m-polar fuzzy graphs, along with several issues. The degree of it is also presented along with edge regularity properties. We also give a relation between m-polar fuzzy antipodal graphs and their underlying crisp graphs. Its properties have also been discussed on m-polar fuzzy odd as well as even cycles, complete graphs, etc. Finally, a real-life application on a road network system in a m-polar fuzzy environment using the $$\mu$$ μ -distance concept is also presented.

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A new fuzzy graph parameter for the comparison of human trafficking chains

Cited by 4 publications

References 29 publications

Adjacent Vertex Distinguishing Coloring of Fuzzy Graphs

Adjacent Vertex Distinguishing Coloring of Fuzzy Graphs

A fuzzy planar subgraph formation model for partitioning very large-scale integration networks

Solution of road network problem with the help of m-polar fuzzy graph using isometric and antipodal concept

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