γ-Edge Irregular Intuitionistic Fuzzy Graph

Abstract

When available knowledge is unable to convey ambiguity using sets, intuitionistic fuzzy sets can be considered as a different technique. In a fuzzy set, just the element membership degree is considered, while in intuitionistic fuzzy Edge irregular intuitionistic fuzzy graph, edge totally irregular intuitionistic fuzzy graph, sets, both membership and non-membership degrees are included. Intuitionistic fuzzy graph is a more advanced fuzzy graph idea. In this thesis degree of an edge 𝜅𝐺(𝑦𝑖𝑦𝑗) = (𝜅1𝐺(𝑦𝑖𝑦𝑗), 𝜅2𝐺(𝑦𝑖𝑦𝑗) of an intuitionistic fuzzy graph, total degree of an edge 𝑡𝜅𝐺(𝑦𝑖𝑦𝑗) = (𝑡𝜅1𝐺(𝑦𝑖𝑦𝑗), 𝑡𝜅2𝐺(𝑦𝑖𝑦𝑗) and operations (complement, union and join) on an intuitionistic fuzzy graph are define. Edge irregular intuitionistic fuzzy graph, edge totally irregular intuitionistic fuzzy graph, highly edge irregular intuitionistic fuzzy graph, highly edge totally irregular intuitionistic fuzzy graph, strongly edge irregular intuitionistic fuzzy graph and strongly edge totally irregular intuitionistic fuzzy graph are also defined with suitable illustration. On an intuitionistic fuzzy graph, such as a γ-edge irregular intuitionistic fuzzy graph, we examine and discuss properties. Moreover, we are establishing results and providing various examples to help understand these concepts.