1-Quasi Total Fuzzy Graph and Its Total Coloring

Fekadu Tesgera Agama; Venkata Naga Srinivasa Rao Repalle

doi:doi:10.11648/j.pamj.20200901.12

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1-Quasi Total Fuzzy Graph and Its Total Coloring

Fekadu Tesgera Agama, Venkata Naga Srinivasa Rao Repalle

Published in Pure and Applied Mathematics Journal (Volume 9, Issue 1)

Received: 27 November 2019 Accepted: 21 December 2019 Published: 17 January 2020

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Abstract

The fuzzy graph theory, its properties, total coloring and applications are currently climbing up. With this concept of fuzzy graph, total fuzzy graph is defined and its properties as well as fuzzy total colorings have been well discussed and studied. Similarly the theory of crisp graph, its properties, applications and colorings are well considered. Moreover, 1-quasi total graphs for crisp graphs, their properties and colorings were discussed by some researchers and the bounds for its total coloring have been established. In this manuscript, from the concept of fuzzy graph we introduced the definition of 1-quasi total graph for fuzzy graphs. To elaborate the definition we provide practical example of fuzzy graph and from this graph we construct the 1-quasi total fuzzy graph of the given fuzzy graph, so that the definition to be meaning full and their relationships can be easily observed from the sketched graphs. In addition some theorems related to the properties of 1-quasi total fuzzy graphs are stated and proved. The results of these theorems are compared with the results obtained from total fuzzy graphs, so that the differences and similarities that 1-quasi total fuzzy graph can have with that of total fuzzy graphs are revealed. Moreover, we define 1-quasi total coloring of fuzzy total graphs and give an example of total coloring of 1-quasi total graphs.

Published in	Pure and Applied Mathematics Journal (Volume 9, Issue 1)
DOI	10.11648/j.pamj.20200901.12
Page(s)	9-15
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Fuzzy Graph, Total Fuzzy Graph, 1-Quasi Total Fuzzy Graph, Total Coloring

References

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[7]	Graph Equations for Line Graphs, Total Graphs, Middle Graphs and Quasi-Total Graphs. D. V. S. Sastry, B. Syam Prasad Raju. 1984, Discrete Mathematics, Vol. 48, pp. 113-119.
[8]	A Discussion for Bounds for 1-quasi Total Colourings. R. V. N. Sirnvasarao, J. VenkateswaraRao. 6, 2012, International Journal of Mathematical Archive, Vol. 3, pp. 2314-2320.
[9]	Fuzzy Graphs, In Fuzzy Sets and their Application to Cognitive and Decision Process. Rosenfield, A. New York: Academic Press, 1975, pp. 77-95.
[10]	Fuzzy Sets, Information and Control. A. Zadeh, Lofti. 1965, Vol. 8, pp. 338-353.
[11]	Vertex Strength of Fuzzy Graphs. Eslahchi, B. N. Onagh. 2006, International Journal of Mathematics and Mathematical Science.
[12]	Fuzzy Total Coloring of Fuzzy Graphs. S. Lavanya, R. Sattanathan. 3, 2009, International Journal of Information Technology and Knowledge Management, Vol. 2, pp. 37-39.
[13]	Fuzzy Cgromatic Number of Line, Total and Middle Graphs of Fuzzy Complete Graphs. S. Kavitha, S. Lavanya. 2, 2014, Annas of Pure and Applied Mathematics, Vol. 8, pp. 251-260.
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[18]	Total Chromatic Number of Middle and Total Graph of Path and Sunlet Graph. Jayaraman, D. Muthuramakrishnan G. 4, 2018, International Journal of Scientific and Innovative Mathematical Research (IJSIMR), Vol. 6, pp. 1-9.

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Fekadu Tesgera Agama, Venkata Naga Srinivasa Rao Repalle. (2020). 1-Quasi Total Fuzzy Graph and Its Total Coloring. Pure and Applied Mathematics Journal, 9(1), 9-15. https://doi.org/10.11648/j.pamj.20200901.12

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ACS Style

Fekadu Tesgera Agama; Venkata Naga Srinivasa Rao Repalle. 1-Quasi Total Fuzzy Graph and Its Total Coloring. Pure Appl. Math. J. 2020, 9(1), 9-15. doi: 10.11648/j.pamj.20200901.12

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AMA Style

Fekadu Tesgera Agama, Venkata Naga Srinivasa Rao Repalle. 1-Quasi Total Fuzzy Graph and Its Total Coloring. Pure Appl Math J. 2020;9(1):9-15. doi: 10.11648/j.pamj.20200901.12

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@article{10.11648/j.pamj.20200901.12,
  author = {Fekadu Tesgera Agama and Venkata Naga Srinivasa Rao Repalle},
  title = {1-Quasi Total Fuzzy Graph and Its Total Coloring},
  journal = {Pure and Applied Mathematics Journal},
  volume = {9},
  number = {1},
  pages = {9-15},
  doi = {10.11648/j.pamj.20200901.12},
  url = {https://doi.org/10.11648/j.pamj.20200901.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20200901.12},
  abstract = {The fuzzy graph theory, its properties, total coloring and applications are currently climbing up. With this concept of fuzzy graph, total fuzzy graph is defined and its properties as well as fuzzy total colorings have been well discussed and studied. Similarly the theory of crisp graph, its properties, applications and colorings are well considered. Moreover, 1-quasi total graphs for crisp graphs, their properties and colorings were discussed by some researchers and the bounds for its total coloring have been established. In this manuscript, from the concept of fuzzy graph we introduced the definition of 1-quasi total graph for fuzzy graphs. To elaborate the definition we provide practical example of fuzzy graph and from this graph we construct the 1-quasi total fuzzy graph of the given fuzzy graph, so that the definition to be meaning full and their relationships can be easily observed from the sketched graphs. In addition some theorems related to the properties of 1-quasi total fuzzy graphs are stated and proved. The results of these theorems are compared with the results obtained from total fuzzy graphs, so that the differences and similarities that 1-quasi total fuzzy graph can have with that of total fuzzy graphs are revealed. Moreover, we define 1-quasi total coloring of fuzzy total graphs and give an example of total coloring of 1-quasi total graphs.},
 year = {2020}
}

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TY  - JOUR
T1  - 1-Quasi Total Fuzzy Graph and Its Total Coloring
AU  - Fekadu Tesgera Agama
AU  - Venkata Naga Srinivasa Rao Repalle
Y1  - 2020/01/17
PY  - 2020
N1  - https://doi.org/10.11648/j.pamj.20200901.12
DO  - 10.11648/j.pamj.20200901.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 9
EP  - 15
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20200901.12
AB  - The fuzzy graph theory, its properties, total coloring and applications are currently climbing up. With this concept of fuzzy graph, total fuzzy graph is defined and its properties as well as fuzzy total colorings have been well discussed and studied. Similarly the theory of crisp graph, its properties, applications and colorings are well considered. Moreover, 1-quasi total graphs for crisp graphs, their properties and colorings were discussed by some researchers and the bounds for its total coloring have been established. In this manuscript, from the concept of fuzzy graph we introduced the definition of 1-quasi total graph for fuzzy graphs. To elaborate the definition we provide practical example of fuzzy graph and from this graph we construct the 1-quasi total fuzzy graph of the given fuzzy graph, so that the definition to be meaning full and their relationships can be easily observed from the sketched graphs. In addition some theorems related to the properties of 1-quasi total fuzzy graphs are stated and proved. The results of these theorems are compared with the results obtained from total fuzzy graphs, so that the differences and similarities that 1-quasi total fuzzy graph can have with that of total fuzzy graphs are revealed. Moreover, we define 1-quasi total coloring of fuzzy total graphs and give an example of total coloring of 1-quasi total graphs.
VL  - 9
IS  - 1
ER  -

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Author Information

Fekadu Tesgera Agama

Department of Mathematics, College of Natural and Computational Science, Wollega University, Nekemte, Ethiopia
Venkata Naga Srinivasa Rao Repalle

Department of Mathematics, College of Natural and Computational Science, Wollega University, Nekemte, Ethiopia

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APA Style

Fekadu Tesgera Agama, Venkata Naga Srinivasa Rao Repalle. (2020). 1-Quasi Total Fuzzy Graph and Its Total Coloring. Pure and Applied Mathematics Journal, 9(1), 9-15. https://doi.org/10.11648/j.pamj.20200901.12

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ACS Style

Fekadu Tesgera Agama; Venkata Naga Srinivasa Rao Repalle. 1-Quasi Total Fuzzy Graph and Its Total Coloring. Pure Appl. Math. J. 2020, 9(1), 9-15. doi: 10.11648/j.pamj.20200901.12

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AMA Style

Fekadu Tesgera Agama, Venkata Naga Srinivasa Rao Repalle. 1-Quasi Total Fuzzy Graph and Its Total Coloring. Pure Appl Math J. 2020;9(1):9-15. doi: 10.11648/j.pamj.20200901.12

Copy | Download

@article{10.11648/j.pamj.20200901.12,
  author = {Fekadu Tesgera Agama and Venkata Naga Srinivasa Rao Repalle},
  title = {1-Quasi Total Fuzzy Graph and Its Total Coloring},
  journal = {Pure and Applied Mathematics Journal},
  volume = {9},
  number = {1},
  pages = {9-15},
  doi = {10.11648/j.pamj.20200901.12},
  url = {https://doi.org/10.11648/j.pamj.20200901.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20200901.12},
  abstract = {The fuzzy graph theory, its properties, total coloring and applications are currently climbing up. With this concept of fuzzy graph, total fuzzy graph is defined and its properties as well as fuzzy total colorings have been well discussed and studied. Similarly the theory of crisp graph, its properties, applications and colorings are well considered. Moreover, 1-quasi total graphs for crisp graphs, their properties and colorings were discussed by some researchers and the bounds for its total coloring have been established. In this manuscript, from the concept of fuzzy graph we introduced the definition of 1-quasi total graph for fuzzy graphs. To elaborate the definition we provide practical example of fuzzy graph and from this graph we construct the 1-quasi total fuzzy graph of the given fuzzy graph, so that the definition to be meaning full and their relationships can be easily observed from the sketched graphs. In addition some theorems related to the properties of 1-quasi total fuzzy graphs are stated and proved. The results of these theorems are compared with the results obtained from total fuzzy graphs, so that the differences and similarities that 1-quasi total fuzzy graph can have with that of total fuzzy graphs are revealed. Moreover, we define 1-quasi total coloring of fuzzy total graphs and give an example of total coloring of 1-quasi total graphs.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - 1-Quasi Total Fuzzy Graph and Its Total Coloring
AU  - Fekadu Tesgera Agama
AU  - Venkata Naga Srinivasa Rao Repalle
Y1  - 2020/01/17
PY  - 2020
N1  - https://doi.org/10.11648/j.pamj.20200901.12
DO  - 10.11648/j.pamj.20200901.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 9
EP  - 15
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20200901.12
AB  - The fuzzy graph theory, its properties, total coloring and applications are currently climbing up. With this concept of fuzzy graph, total fuzzy graph is defined and its properties as well as fuzzy total colorings have been well discussed and studied. Similarly the theory of crisp graph, its properties, applications and colorings are well considered. Moreover, 1-quasi total graphs for crisp graphs, their properties and colorings were discussed by some researchers and the bounds for its total coloring have been established. In this manuscript, from the concept of fuzzy graph we introduced the definition of 1-quasi total graph for fuzzy graphs. To elaborate the definition we provide practical example of fuzzy graph and from this graph we construct the 1-quasi total fuzzy graph of the given fuzzy graph, so that the definition to be meaning full and their relationships can be easily observed from the sketched graphs. In addition some theorems related to the properties of 1-quasi total fuzzy graphs are stated and proved. The results of these theorems are compared with the results obtained from total fuzzy graphs, so that the differences and similarities that 1-quasi total fuzzy graph can have with that of total fuzzy graphs are revealed. Moreover, we define 1-quasi total coloring of fuzzy total graphs and give an example of total coloring of 1-quasi total graphs.
VL  - 9
IS  - 1
ER  -

Copy | Download