Near Mean Labeling in Dicyclic Snakes

Abstract

K. Palani et al. defined the concept of near mean labeling in digraphs. Let D=(V,A) be a digraph where Vthe vertex is set and A is the arc set. Let f:V\rightarrow{0,\ 1,\ 2,\ \ldots,q} be a 1-1 map. Define f^\ast:A\rightarrow{1,\ 2,\ \ldots,q} byf^\ast\left(e=\vec{uv}\right)=\left\lceil\frac{f\left(u\right)+f(v)}{2}\right\rceil. Letf^\ast\left(v\right)=\left|\sum_{w\in V}{f^\ast(\vec{vw})}-\sum_{w\in V}{f^\ast(\vec{wv})}\right|. Iff^\ast\left(v\right)\le2\ \ \forall\ v\in A(D), then f is said to be a near mean labeling of D and D is said to be a near mean digraph. In this paper, different dicyclic snakes are defined and the existence of near mean labeling in them is checked.

Keywords

• near mean,labeling, digraphs, di-cyclic, di-quadrilateral, di-pentagonal, snake.