Abstract
In this paper, neighbourly irregular fuzzy graphs, neighbourly total irregular fuzzy graphs, highly irregular fuzzy graphs and highly total irregular fuzzy graphs are introduced. A necessary and sufficient condition under which neighbourly irregular and highly irregular fuzzy graphs are equivalent is provided. We define d2 degree of a vertex in fuzzy graphs and total d2 -degree of a vertex in fuzzy graphs and (2, k)-regular fuzzy graphs, totally (2, k)- regular fuzzy graphs are introduced. (2, k)- regular fuzzy graphs and totally (2, k)-regular fuzzy graphs are compared through various examples.
Highlights
In 1975, Rosenfeld considered fuzzy relations on fuzzy sets
Fuzzy graph is an expression of fuzzy relation and the fuzzy graph is frequently expressed in fuzzy matrix
We define d2 degree of a vertex in fuzzy graphs and total d2 -degree of a vertex in fuzzy graphs and (2, k)-regular fuzzy graphs, totally (2, k)- regular fuzzy graphs are introduced. (2, k)- regular fuzzy graphs and totally (2, k)-regular fuzzy graphs are compared through various examples
Summary
In 1975, Rosenfeld considered fuzzy relations on fuzzy sets. He developed the theory of fuzzy graphs. Definition 1.7 An undirected graph is called connected if there is a path between every pair of distinct vertices of the graph. Example 1.4 The graph G1 in Figure (6) is connected, because for every pair of distinct vertices there is a path between them. FtbpFU3.4108in1.6302in0ptSubgraphs of the original graph3.7Figure(3.7) Definition 1.9 The degree of an edge (u, v) in the underlying graph is defined as dG(u, v) = dG(u) + dG(v) − 2. Definition 1.10 A graph G is called regular if every vertex is adjacent only to vertices having the same degree. A graph G is called irregular, if there is a vertex which is adjacent only to vertices with distinct degrees. In figure (7) he original graph is regular fuzzy graph, because every vertex is adjacent only to vertices having the same degree
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
