Abstract
Connectivity index CI has a vital role in real-world problems especially in Internet routing and transport network flow. Intuitionistic fuzzy graphs IFGs allow to describe two aspects of information using membership and nonmembership degrees under uncertainties. Keeping in view the importance of CI s in real life problems and comprehension of IFGs , we aim to develop some CI s in the environment of IFGs . We introduce two types of CI s , namely, CI and average CI , in the frame of IFGs . In spite of that, certain kinds of nodes called IF connectivity enhancing node IFCEN , IF connectivity reducing node IFCRN , and IF neutral node are introduced for IFGs . We have introduced strongest strong cycles, θ -evaluation of vertices, cycle connectivity, and CI of strong cycle. Applications of the CI s in two different types of networks are done, Internet routing and transport network flow, followed by examples to show the applicability of the proposed work.
Highlights
Zadeh [1] presented the idea of fuzzy set (FS) by giving membership grades to the objects of a set ranging from zero to one
Let C denote a cycle in an Intuitionistic fuzzy graphs (IFGs) G. en, C is called IF strongest strong cycle (IFSSC) if it is the union of two strongest strong u − v paths for each of u and v in C with the exception when uv in C is an IF bridge of G
We have developed some Connectivity index (CI) in the IFGs framework due to the reason that IFGs cover uncertainty and vagueness with the help of two membership grades
Summary
Zadeh [1] presented the idea of fuzzy set (FS) by giving membership grades to the objects of a set ranging from zero to one. 2. Preliminaries roughout this section, definitions and examples are presented to recall concepts related to IFG, arcs in IFG, and IF-cycles relevant to the present work. E concept of strong and weakest edges is of much importance in IFGs as well as in our study. An edge (ui, uj) in an IFG is (1) Strong if TM(ui, uj) ≥ CONNT(G)(ui, uj) and FM(ui, uj) ≤ CONNF(G)(ui, uj) for each ui, uj ∈ V (2) Weakest if TM(ui, uj) < CONNT(G)(ui, uj) and FM(ui, uj) > CONNF(G)(ui, uj) for each ui, uj ∈ V e coming definition gives us the strongest paths between two vertices. That is why we aim to propose the concepts of several CIs for IFGs and study their applications
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