Hexagonal Snakes With Alpha Labeling Along A Path

Abstract

Abstract The graceful labeling of a graph G with p vertices and q edges is an injection f: V (G) to {0, 1, 2… q} such that, when each edge uv is assigned the label |f (u)-f (v)|. The resulting edge set are {1, 2, 3 …q}. When graceful Labeling is applied to a graph it is known as a Gracful graph. In this paper, we introduce the graph HSn by arranging a series of Hexagons glued to each other by attaching the any one vertex of the first hexagon to the next one and the second hexagon to the third one and so on which is called a Hexagonal Snake. Thus, ‘n’ number of of hexagonal snakes are fixed along a path. We have applied graceful labeling to this Hexagonal Snake graph and have shown that it satisfies α-labeling.