Median vertex vague labeling of vague graphs

Abstract

Vague graph is a pair $G=(A, B)$ where $A=\left(t_A, f_A\right)$ is a vague set on $V$ and $B=\left(t_B, f_B\right)$ is a vague set on $E \subseteq V \times V$ such that $t_B(x y) \leq \min \left(t_A(x), t_A(y)\right)$ and $f_B(x y) \geq \max \left(f_A(x), f_A(y)\right)$ for each edge $x y \subseteq E . A$ is called as the vague vertex set of $G$ and $B$ as the vague edge set of $G$. The main purpose of this paper is to introduce Median Vertex Vague Labeling of vague graphs. In addition, an application of Median Vertex Vague Labeling in traffic flow network is discussed in this paper.