Totally Regular Fuzzy Graphs
Keywords:
Total degree of a vertex, Complement of fuzzy graph, Complete graph
Abstract
In this paper, some properties of total degree and totally regular fuzzy graphs are discussed. They are illustrated through various examples. It is proved that every fuzzy graph is an induced subgraph of a totally regular fuzzy graph. The procedure described in the proof is illustrated through an example. Also the total degree of a vertex in fuzzy graphs formed by the operation Union in terms of the total degree of vertices in the given fuzzy graphs for some particular cases are obtained. Using them, their totally regular property is studied.
References
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John N.Modeson, Premch and S.Nair, Fuzzy Graphs and Fuzzy Hypergraphs, Physica-verlag, Heidelberg, (2000).
L.A.Zadeh, Fuzzy Sets, Inform. Control., 8(1965), 338-53.
J.N.Mordeson and C.S.Peng, Operations on Fuzzy Graphs, Inform. Sci., 79(1994), 159-170.
A.Nagoorgani and M.BasheerAhamed, Order and Size in Fuzzy Graph, Bulletin of Pure and Applied Sciences, 22E(1)(2003), 145-148.
A.Nagoorgani and K.Radha, Some Sequences in Fuzzy Graphs, Far East Journal of Applied Mathematics, 31(3)(2008), 321-335.
A.Nagoorgani and K.Radha, On Regular Fuzzy Graphs, Journal of Physical Sciences, 12(2008), 33-40.
A.Nagoorgani and K.Radha, The Degree of a vertex in some fuzzy graphs, International Journal of Algorithms, Computing and Mathematics, 3(2009).
A.Rosenfeld, Fuzzy Graphs, In: L. A. Zadeh, K.S. Fu, M. Shimura, Eds., Fuzzy sets and Their Applications, Academic Press, (1975), 77-95.
K.Radha and M.Vijaya, The Total Degree of a vertex in some fuzzy graphs, Jamal Academic Research Journal : An Interdisciplinary, special issue, (2014), 160-168.
A.Nagoorgani and B.Fathima Kani, Degree of a vertex in Alpha, Beta, Gamma Product of Fuzzy Graphs, Jamal Academic Research Journal : An Interdisciplinary, special issue, (2014), 104-114.
K.Radha and M.Vijaya, Totally Regular Property of Cartesian Product of two fuzzy graphs, Jamal Academic Research Journal : An Interdisciplinary, special issue, (2015), 647-652.
K.Radha and M.Vijaya, Totally Regular Property of Composition of two fuzzy graphs”, International journal of Pure and Applied Mathematical Sciences, 8(1)(2015), 87-100.
K.Radha and M.Vijaya, Totally Regular Property of the join of two fuzzy graphs, International journal of Fuzzy Mathematical Archieve, 8(1)(2015), 9-17.
K.Radha and M.Vijaya, Totally Regular Property of Alpha Product of two fuzzy graphs, International Journal of Multidisciplinary Research and Development, 3(4)(2016), 125-130.
K.Radha and M.Vijaya, Totally Regular Property of Conjunction of two fuzzy graphs, Jamal Academic Research journal : An Interdisciplinary, special issue, (2016), 157-163.
K.Radha and M.Vijaya, Regular and totally regular property of disjunction of two fuzzy graphs, International Journal of Multidisciplinary Research and Development, 4(4)(2017), 63-71.
John N.Modeson, Premch and S.Nair, Fuzzy Graphs and Fuzzy Hypergraphs, Physica-verlag, Heidelberg, (2000).
L.A.Zadeh, Fuzzy Sets, Inform. Control., 8(1965), 338-53.
J.N.Mordeson and C.S.Peng, Operations on Fuzzy Graphs, Inform. Sci., 79(1994), 159-170.
A.Nagoorgani and M.BasheerAhamed, Order and Size in Fuzzy Graph, Bulletin of Pure and Applied Sciences, 22E(1)(2003), 145-148.
A.Nagoorgani and K.Radha, Some Sequences in Fuzzy Graphs, Far East Journal of Applied Mathematics, 31(3)(2008), 321-335.
A.Nagoorgani and K.Radha, On Regular Fuzzy Graphs, Journal of Physical Sciences, 12(2008), 33-40.
A.Nagoorgani and K.Radha, The Degree of a vertex in some fuzzy graphs, International Journal of Algorithms, Computing and Mathematics, 3(2009).
A.Rosenfeld, Fuzzy Graphs, In: L. A. Zadeh, K.S. Fu, M. Shimura, Eds., Fuzzy sets and Their Applications, Academic Press, (1975), 77-95.
K.Radha and M.Vijaya, The Total Degree of a vertex in some fuzzy graphs, Jamal Academic Research Journal : An Interdisciplinary, special issue, (2014), 160-168.
A.Nagoorgani and B.Fathima Kani, Degree of a vertex in Alpha, Beta, Gamma Product of Fuzzy Graphs, Jamal Academic Research Journal : An Interdisciplinary, special issue, (2014), 104-114.
K.Radha and M.Vijaya, Totally Regular Property of Cartesian Product of two fuzzy graphs, Jamal Academic Research Journal : An Interdisciplinary, special issue, (2015), 647-652.
K.Radha and M.Vijaya, Totally Regular Property of Composition of two fuzzy graphs”, International journal of Pure and Applied Mathematical Sciences, 8(1)(2015), 87-100.
K.Radha and M.Vijaya, Totally Regular Property of the join of two fuzzy graphs, International journal of Fuzzy Mathematical Archieve, 8(1)(2015), 9-17.
K.Radha and M.Vijaya, Totally Regular Property of Alpha Product of two fuzzy graphs, International Journal of Multidisciplinary Research and Development, 3(4)(2016), 125-130.
K.Radha and M.Vijaya, Totally Regular Property of Conjunction of two fuzzy graphs, Jamal Academic Research journal : An Interdisciplinary, special issue, (2016), 157-163.
K.Radha and M.Vijaya, Regular and totally regular property of disjunction of two fuzzy graphs, International Journal of Multidisciplinary Research and Development, 4(4)(2017), 63-71.
How to Cite
K.Radha, & M.Vijaya. (2017). Totally Regular Fuzzy Graphs. International Journal of Current Research in Science and Technology, 3(8), 11-18. Retrieved from https://crst.gfer.org/index.php/crst/article/view/94
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