reza shahverdi - Department of Mathematics, Islamic Azad University Qaemshahr branch, Iran.

A graph structure is a useful tool in solving the combinatorial problems in different areas of computer science and computational intelligence systems. In this paper, we apply the concept of vague sets to graph structures. We introduce certain notions, including vague graph structure (VGS), strong vague graph structure, vague i-cycle, and illustrate these notions by several examples. We study ϕ-complement, self-complement, strong self-complement, totally strong self-complement in vague graph structures, and investigate some of their properties. Finally, an application of vague infuence graph structure is given.

Vague set, Vague Graph Structure, strong (VGS), ϕ-complement of a VGS