Computation of Lucky Number of Comb Graphs Cfw, Cgw, Chw and Triangular Snake, Alternate Triangular Snake Graphs

Abstract

Let λ:V(Ω)→{1, 2,..., z} be a mapping of vertices of a graph Ω. Let S(x) denote the sum of labels of the neighbors of the vertex x in Ω. If vertex x has degree zero, we put S(x)=0. A mapping λ is categorized as lucky labeling if S(x)=S(y) for every pair of adjacent vertices x and y. The lucky number of graph Ω, denoted by η (Ω), is the least positive integer z used to label vertices to form lucky labeling. In this paper, we demonstrate that different families of comb graph and snake graph are lucky labeled graphs. We also calculate the exact value of the lucky number for the aforementioned graphs.