Introduction a graph is a convenient way of representing information involving relationship between objects. Recall the definition ofa fuzzy bridge definition 1. One way to consider these fuzzy incompatibilities is to define a coloring function for fuzzy graphs. Today, fuzzy graphs are the basic mathematical structure in such areas of research that include clustering analysis, group. Myna, abstract in this paper, we use a fuzzy graph model to represent a traffic network of a city and discuss a method to find the different type of accidental zones. In general, graph theory has a wide range of applications in diverse fields.
Mathew on blocks and stars in fuzzy graphs 1665 5 k. Here we define fuzzy graphs with fuzzy vertex set and fuzzy edge set. Let 1 2, s b b b n be the number of blocks of g and m. The 2dominating set d of a graph is defined as if for every node v. Strong neighbours, 2 dominating set, 2 dominat ion number ams mathematics subject classification 2010. A comparative study between neighbourly irregular and highly irregular fuzzy graphs is made. A graph g that requires different color for its proper colorings. Then by definition split domination does not exists. A more detailed discussion of fuzzy graphs is found in 3. One way is to define the distance disx,y between x and y as the length of. Now assume g is a fuzzy graph with at least 2 blocks. Complement properties of tensor product of strong fuzzy.
So we are mainly going to deal in fuzzy model data matrices which are got from feelings, not always concrete numbers. Mainly focused on fuzzy trees defined by rosenfeld in 10, several other types of fuzzy trees are defined depending on the acyclicity level of a fuzzy graph. The concept of strong arcs in fuzzy graphs was discussed in 8. We now provide two popular ways of defining the distance between a pair of vertices. Direct sum of n pythagorean fuzzy graphs with application to group decisionmaking article pdf available in journal of multiplevalued logic and soft computing 3312. Intuition that the results known so far on energy of a graph might be a particular case of more general. Vijaya department of mathematics, marudupandiyar college, thanjavur, tamil nadu, india 6403 abstract in this work we introduce the complement of. Many problems of practical interest can be modeled and solved by using graph algorithms.
First let us recall some preliminary definitions that can be found in 19. Fuzzy logic and the theory of fuzzy sets have been applied widely in areas like information theory, pattern recognition, clustering, expert systems, database theory, control theory, robotics. It is observed that there are selfcentered fuzzy trees. Bhutani department of mathematics, the catholic university of america. Similarly, a fuzzy graph is a symmetric binary fuzzy relation on a fuzzy subset. Pdf on blocks and stars in fuzzy graphs researchgate. The elements of v are thought of as vertices of the graph and the elements of r are thought of as the edges similarly, any fuzzy. In this paper we give the role of fuzzy graphs in fuzzy models like fuzzy cognitive maps fcms, fuzzy relational maps frms and fuzzy relational equations fres. Akram introduced the concept of bipolar fuzzy graphs in 1, he discussed the concept of isomorphism of these graphs, and investigated some of their important. Rosenfeld, fuzzy end nodes in fuzzy graphs, information sciences 152 2003, 323326. We propose certain types of intervalvalued fuzzy graphs including balanced intervalvalued fuzzy graphs, neighbourly irregular intervalvalued fuzzy graphs, neighbourly total irregular intervalvalued fuzzy. In this paper we define the fuzzy chromatic number, chromatic index and fuzzy total chromatic number of a fuzzy graph as fuzzy numbers through the cuts of the fuzzy graph which are crisp graphs. Fuzzy graph model for assignment problem 163 this assignment problem can be solved by finding a complete matching of fuzzy bipartite graph of g.
No two fuzzy bridges in a block can have a common nodetheorem 2. In 2009, mathew and sunitha 18,19 introduced the concepts of fuzzy arc cuts and fuzzy node cuts to generalize cuts in graphs as sets of arcs and nodes, respectively, whose removal from the fuzzy. When the two fuzzy hypergraphs and are same the weak isomorphism between them becomes an isomorphism and. Pattern recognition letters 9 1989159162 april 1989 northholland on automorphisms of fuzzy graphs kiran r. Example n the darkness of color stands for the strength of relation in a n relation a, b is stronger than that of relation a, c.
The book 5 by mordeson and nair entitled fuzzy graphs and fuzzy hypergraphs is an excellent source for research in fuzzy graphs and fuzzy hypergraphs. Bhutani and battou 10 introduced the concept of mstrong fuzzy graphs with some properties. The exact values of g for some standard fuzzy graphs are found. Vijaya department of mathematics, marudupandiyar college, thanjavur, tamil nadu, india 6403 abstract in this work we introduce the complement of strong fuzzy graph, tensor product of fuzzy graphs and strong fuzzy graph. A visualization experiment for displaying fuzzy graphs rosenfeld 1975, in fuzzy sets and their applications to cognitive and decision processes, page 77. A graph is a pair v, r, where v is a set and r is a relation on v. New concepts of intervalvalued intuitionistic s, t.
All blocks in the fuzzy graph are fuzzy subgraphs of the given fuzzy graph 1. In this paper we discuss about 2dominating set and 2domination number of a fuzzy graph. Fuzzy graph, linear fuzzy graph, fuzzy line graph, product fuzzy graphs. Also some results on neighbourly irregular fuzzy graphs are studied. Fuzzy graphs are the backbone of many real systems like networks, image, scheduling, etc. Introduction fuzzy graphs were introduced by rosenfeld 5. The concept fuzzy graphs was introduced by azriel rosenfeld in 1975 11. Two very important and useful concepts are those of granularity. Since then lots of works on fuzzy graphs have been carried. The cases when g is a fuzzy tree and g is a block are. In the course of fuzzy technological development, fuzzy graph theory was identified quite early on for its importance in making things work. But, it was observed by rosenfeld that a block in a fuzzy. V g v e, in this book, we replace g with v, e g v, e for convenience. But, due to some restriction on edges, fuzzy graphs are limited to represent for some systems.
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