A Study on Vague Graph Structures with an Application

Abstract

Fuzzy graph (FG) models take on the presence being ubiquitous in environmental and fabricated structures by human, specifically the vibrant processes in physical, biological, and social systems. Owing to the unpredictable and indiscriminate data which are intrinsic in real-life, problems being often ambiguous, so it is very challenging for an expert to exemplify those problems through applying an FG. Vague graph structure (VGS), belonging to FGs family, has good capabilities when facing with problems that cannot be expressed by FGs. VGSs have a wide range of applications in the field of psychological sciences as well as the identification of individuals based on oncological behaviors. Therefore, in this paper, we apply the concept of vague sets (VSs) to GS. We define certain notions, VGS, strong vague graph structure (SVGS), and vague ${\beta }_i$ -cycle and describe these notions by several examples. Likewise, we introduce $\psi$ -complement, self-complement (SC), strong self-complement (SSC), and totally strong self-complement (TSSC) in VGS and investigate some of their properties. Finally, an application of VGS is presented.