Ganesh Ghorai

A study on m-polar fuzzy planar graphs

In many practical applications with a graph structure, there may exist crossing between edges which is not allowed in a crisp planar graph. Considering that graphic structures can be used to describe the crossing of edges in an m-polar fuzzy multi-graph with certain amount of m-polar fuzzy planarity value, first of all the notion of m-polar fuzzy multi-set is introduced. Then m-polar fuzzy multi-graphs, m-polar fuzzy planar graphs and m-polar fuzzy strong edges are defined. Several properties of m-polar fuzzy planar graphs are also studied.

Faces and dual of m-polar fuzzy planar graphs

Recently, Ghorai and Pal (12) introduced the notion of m-polar fuzzy planar graphs using the concept of m-polar fuzzy multisets. In this paper, m-polar fuzzy faces and strong m-polar fuzzy faces are defined. Then m-polar fuzzy dual graph of an m-polar fuzzy planar graph is introduced with example. Some isomorphism properties of m-polar fuzzy planar graphs are also studied.

Some isomorphic properties of m-polar fuzzy graphs with applications

Abstract The theory of graphs are very useful tool in solving the combinatorial problems in different areas of computer science and computational intelligence systems. In this paper, we present a frame work to handle m-polar fuzzy information by combining the theory of m-polar fuzzy sets with graphs. We introduce the notion of weak self complement m-polar fuzzy graphs and establish a necessary condition for m-polar fuzzy graph to be weak self complement. Some properties of self complement and weak self complement m-polar fuzzy graphs are discussed. The order, size, busy vertices and free vertices of an m-polar fuzzy graphs are also defined and proved that isomorphic m-polar fuzzy graphs have same order, size and degree. Also, we have presented some results of busy vertices in isomorphic and weak isomorphic m-polar fuzzy graphs. Finally, a relative study of complement and operations on m-polar fuzzy graphs have been made. Applications of m-polar fuzzy graph are also given at the end.

Regular product vague graphs and product vague line graphs

Abstract Vague graph is a generalized structure of fuzzy graph which gives more precision, flexibility, and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we introduced the notion of regular, totally regular product vague graphs, and product vague line graph. We proved that under some conditions regular and totally regular product vague graph becomes equivalent. Some properties of product vague line graph are investigated. We showed that a product vague graph is isomorphic to its corresponding product vague line graph under some conditions.

Application of Strong Arcs in m-Polar Fuzzy Graphs

Recently, m-polar fuzzy graph (mPF graph) becomes a growing research topic as the generalization of fuzzy graph. In this paper, at first mPF path, mPF cycle in an mPF graph are defined. The strength of connectedness of mPF path is introduced. Next, strongest and strong mPF path, mPF bridges, mPF cut nodes, mPF tree and mPF forests in an mPF graph are considered. Also, it is proved that an arc of mPF tree is strong mPF arc if and only if it is an mPF bridge. Finally, mPF end nodes in an mPF graph is defined and investigated some properties of it. An application of strongest path problem in 3-polar fuzzy graph is also given at the end.