Certain Concepts of Vague Graphs With Applications to Medical Diagnosis

The purpose of this research study is to present and explore the key properties of some new operations on vague graphs, including rejection, maximal product, symmetric difference, and residue product. This article introduces the notions of degree of a vertex and total degree of a vertex in a vague graph. As well, this study outlines the specific conditions required for obtaining the degrees of vertices in vague graphs under the operations of maximal product, symmetric difference, and rejection. The article also discusses applications of vague sets in medical diagnosis.