DEGREE OF INTUITIONISTIC L-FUZZY GRAPH

unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract. In this paper we continue the studies related to Intuitionistic L Fuzzy Graph which is a generalisation of Intuitionistic Fuzzy Graph.We try to define the connectivity of vertices and edges in Intuitionistic L Fuzzy Graph. We also try to define the degree of a vertex in an Intuitionistic L Fuzzy Graph and its properties.


INTRODUCTION
There has been an unprecedented progress in the study of Graph Theory in the twentieth century. Real world problems have often been analysed and studied successfully using Graphs.
These problems and other famous puzzles have resulted in development in various topics in Graph theory. Eulerian graph theory is inspired from the famous Konigsberg bridge problem.
Rosenfeld in his classical paper introduced the concept of fuzzy graphs as a means to model various real life situations. An L-fuzzy set is a set in which the range[0,1] is replaced by a lattice, according to Klir and Yuan. Pramada Ramachandranand K V Thomas introduced the concept of L-Fuzzy graph. Isomorphism and associated matrices of L-fuzzy graph were studied by them.
Intutionistic fuzzy sets were introduced as a generalisation of fuzzy sets by Atanassov [3] in 1983 along with the concept of intutionistic fuzzy graph. M G Karunambigai and R Parvathi [4] [5] introduced the concept of fuzzy graph elaborately and analysed its components. Akram et al described the properties of strong intutionistic fuzzy graphs,intutionistic fuzzy cycle and intutionistic fuzzy trees [6] [7]. A Nagoor Gani and S Shajitha Begum examined the properties of various types of degrees, order and size of IFG.
In this paper we studied the degree and other properties of Intutionistic L fuzzy graphs. We have continued on our work detailed in our paper titled 'Intutionistic L-fuzzy graph' Let G=(V,E) be an IFG.Then the degree of a vertex v is defined by denote the membership and non membership of an edge (vi,vj) in E respectively. Then the degree of the graph is equal to

Definition
Then the degree of the graph   0 ) 3.9. Definition. A Complete Intuitionistic L Fuzzy Graph is an Intuitionistic L Fuzzy Graph 3.11. Theorem. Let G 1L and G 2L be two Intuitionistic L Fuzzy Graphs and G L be the union ) be the degree of vertex v in G 1L , G 2L and G L respectively. Then d Let G L be the union of G 1L and G 2L .
Let v be an arbitrary vertex in V = V 1 ∪V 2 Then the degree of v in G L is

Remark.
We cannot find an ILFG for every diagonal matrix.
Example : Here G L contains two vertices say v1 and v2.

CONCLUSION
In this paper we defined Intuitionistic L-Fuzzy Graph. Then we defined degree of a vertex in Intuitionistic L-fuzzy graphs. We proved some properties related to degree of vertex in Intuitionistic L-fuzzy graph. We defined the degree of an Intuitionistic L-Fuzzy graph. We have also discussed matrices associated with degree of an Intuitionistic L-Fuzzy graph.There is a scope to introduce more concepts related to degree matrix of an Intuitionistic L Fuzzy Graph.

CONFLICT OF INTERESTS
The author(s) declare that there is no conflict of interests.