Sovan Samanta

Fuzzy k-competition graphs and p-competition fuzzy graphs

Fuzzy competition graph as a generalization of competition graph is introduced here. Two generalizations of fuzzy competition graph as fuzzy k-competition graphs and p-competition fuzzy graphs are also defined. These graphs are related to fuzzy digraphs. Fuzzy neighbourhood graphs, related to fuzzy graphs, are also defined here. Besides, some relations between fuzzy competition graphs and fuzzy neighbourhood graphs have been established. And finally, several results to find strong edges of the above mentioned graphs have also been established.

A study on bipolar fuzzy graphs

Recently, bipolar fuzzy graph is a growing research topic as it is the generalization of fuzzy graphs. In this paper, at first we define three new operations on bipolar fuzzy graphs, viz. direct product, semi strong product and strong product. Likewise, sufficient conditions for each one of them to be complete are given. Also, it is proved that any of the products of strong bipolar fuzzy graphs are strong bipolar fuzzy graphs.

Fuzzy Planar Graphs

Fuzzy planar graph is a very important subclass of fuzzy graph. In this paper, two types of edges are mentioned for fuzzy graphs: effective edges and considerable edges. In addition, a comparative study between Kuratowskis graphs and fuzzy planar graph is made. A new concept of a strong fuzzy planar graph is introduced. Some related results are established. These results have certain applications in subway tunnels, routes, oil/gas pipelines representation, etc. It is also shown that an image can be represented by a fuzzy planar graph, and contraction of such an image can be made with the help of a fuzzy planar graph.

Interval-valued fuzzy planar graphs

In this paper, interval-valued fuzzy planar graphs are defined and several properties are studied. The interval-valued fuzzy graphs are more efficient than fuzzy graphs, since the degree of membership of vertices and edges lie within the interval [0, 1] instead at a point in fuzzy graphs. We also use the term ‘degree of planarity’ to measures the nature of planarity of an interval-valued fuzzy graph. The other relevant terms such as strong edges, interval-valued fuzzy faces, strong interval-valued fuzzy faces are defined here. The interval-valued fuzzy dual graph which is closely associated to the interval-valued fuzzy planar graph is defined. Several properties of interval-valued fuzzy dual graph are also studied. An example of interval-valued fuzzy planar graph is given.

New concepts of fuzzy planar graphs

Fuzzy planar graph is an important subclass of fuzzy graph. Fuzzy planar graphs and its several properties are presented. A very close association of fuzzy planar graph is fuzzy dual graph. This is also defined and several properties of it are studied. Isomorphism on fuzzy graphs are well defined in literature. Isomorphic relation between fuzzy planar graph and its dual graph are established.

Telecommunication System Based on Fuzzy Graphs

Telecommunication is one of the unavoidable utilities of daily life. Telecommunication service providers have data records of its users. These records are represented by crisp graphs. Certain parameters like center persons, churn prediction, etc. are more perfectly calculated if the data are represented by fuzzy graphs. In this paper, we have introduced a fuzzy telecommunication network (FTN) using fuzzy graph theory.Star persons and related terms are defined in this fuzzy telecommunication network.A small example is described to illustrate the network. Churn prediction is a big issue for telecom service providers. This study introduces churn prediction in the fuzzy telecommunication network. New idea on measurement of churn prediction is presented here.

Product of bipolar fuzzy graphs and their degree

The concepts of graph theory are applied in many areas of computer science including data mining, image segmentation, clustering, image capturing and networking. It is also known that lots of uncertainties occur in these areas. To handle the uncertainty that occurs in graph theory, fuzzy graph theory is successfully used in many problems. A bipolar fuzzy set is a generalization of the fuzzy set. In this paper, two new operations on bipolar fuzzy graphs, viz. normal product and tensor product, are defined. Also, the degrees of the vertices of the resultant graphs which are obtained from two given bipolar fuzzy graphs and using the operations Cartesian product, composition, tensor and normal product are determined.

Generalized fuzzy trees

Graphs are the backbone of many real systems like social networks, image segmentation, scheduling, etc. To input uncertainty to such systems, generalized fuzzy graphs are used. Generalized fuzzy tree is one generalized fuzzy subgraph of a generalized fuzzy graph which characterizes the whole graph. In this study, generalized fuzzy trees are introduced. The concepts of strongly connectedness, nearly disconnect, distance between two nodes, bridges are exemplified.

Some more results on fuzzy k-competition graphs

Fuzzy competition graph as the generalization of competition graph is introduced here. Fuzzy k-competition graph as a special type of fuzzy competition graph is defined here along with fuzzy isolated vertices. The fuzzy competition number is also introduced and investigated several properties. Isomorphism properties on fuzzy competition graphs are discussed.

A study on vague graphs

The main purpose of this paper is to introduce the notion of vague h-morphism on vague graphs and regular vague graphs. The action of vague h-morphism on vague strong regular graphs are studied. Some elegant results on weak and co weak isomorphism are derived. Also,