Series and Parallel Connections in Intuitionistic Fuzzy Graphs

In this paper, we introduce two new operations on Min-max Intuitionistic Fuzzy Graphs, namely Parallel and Series connections along with some of its basic properties. Parallel and Series connections between two Min-max Intuitionistic Fuzzy Graphs are constructed and illustrated with relevant examples. Parallel connections and Series connections are obtained by deleting any two edges and introducing a new edge. Definition of Max-max Intuitionistic Fuzzy Graph is also introduced. Construction of Parallel and Series connections between two Min-max Intuitionistic Fuzzy Graphs gives rise to Max-max IFG which is a new type of Intuitionistic Fuzzy Graph where both the membership and non-membership functions of some of the edges are less than or equal to maximum of membership and non-membership functions of their respective incident vertices. It is shown that the number of edges in a Parallel connection is twice the product of edges in the two Min-max Intuitionistic Fuzzy Graphs whereas in a Series connection it is four times the product of edges in the two Min-max Intuitionistic Fuzzy Graphs. The study reveals that any two electrical circuits with its enclosed components (resistors, capacitors etc.) can be represented as vertices of two Min-max Intuitionistic Fuzzy Graphs and their Parallel and Series connections can be generated.