2-Quasitotal Fuzzy Graphs and Their Total Coloring

Repalle, V. N. Srinivasa Rao; Agama, Fekadu Tesgera

doi:10.1155/2020/8814220

Cited by 2 publications

(1 citation statement)

References 11 publications

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“…2-qusi T F G definition, properties, and its coloring are well studied by Fekadu Tesgera Agama and R.V.N. Srinivasa Rao Repalle [16]. Some related studies on line graph of fuzzy graphs, homeomorphisms and others are also used for this study from [15].…”

Section: Introductionmentioning

confidence: 99%

The Isomorphism of Total Fuzzy Graphs

Agama¹,

Repalle²

2022

IJFIS

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This manuscript is aimed to deal with the isomorphism properties of total fuzzy graph. In order to achieve the desired objective, we consider two fuzzy graphs and their total fuzzy graphs. For these total fuzzy graphs, the notion of homomorphism of total fuzzy graphs is defined and the existence of a homomorphism between these two total fuzzy graphs is shown by examples. This is achieved by both sketching their graph and verifying the condition of homomorphism. Having a mapping being a homomorphism of the total fuzzy graphs the concept of weak isomorphism and co-weak isomorphism are presented with separate and distinct definition. These definitions are accompanied with supportive examples and the case where a homomorphism between two total fuzzy graphs is not weak-isomorphism is observed and illustrated by supportive example. In addition to these, the notion of co-weak isomorphism is also defined and illustrated by using a typical example. A very great attention is given to the definition of an isomorphism of total fuzzy graph and results arising from this definition. Accordingly, certain theorems related to isomorphic properties of total fuzzy graphs are stated and each of these theorems are thoroughly proved to show the results. Finally the manuscript states the future research works, limitations of the manuscript.

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Section: Introductionmentioning

confidence: 99%

The Isomorphism of Total Fuzzy Graphs

Agama¹,

Repalle²

2022

IJFIS

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New results of partially total fuzzy graph

Agama

Repalle

Rathour³

2023

BMC Res Notes

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Objective The study of total fuzzy graphs in all cases is crucial for the development of both theories and applications of the graph theory. Without theory the application will not be developed. Hence this manuscript attempted to theorize the conception of partially total fuzzy graphs. Results The article introduced the partially total fuzzy graph by keeping all the conditions of fuzziness as it is. From these definitions, it is endeavored to get the partial total fuzzy graph of a given fuzzy graph which is supported by illustrations. Also, some propositions and theorems related to this concept were developed and proved.

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2-Quasitotal Fuzzy Graphs and Their Total Coloring

Cited by 2 publications

References 11 publications

The Isomorphism of Total Fuzzy Graphs

The Isomorphism of Total Fuzzy Graphs

New results of partially total fuzzy graph

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