(S,d)Magic Labeling of Some Cycle Related Graphs

Abstract

Objective: To examine the existence of (s,d) Magic Labeling on cycle related graphs.
Methods: Let G (p,q) be a simple, non-trivial, connected, undirected graph with p vertices and q edges. Let f:V(G)→{s,s+d,s+2d,..s+(q+1)d} and g:E(G)→{d,2d,3d…2(q-1)d} be an injective function. Then, for any u,v∈V(G) and uv∈E(G),f(u)+g(uv)+f(v) is a constant, and the function f is said to be (s, d) magic labeling. If a graph G admits (s,d) magic labeling, then it is referred to as a (s,d) magic graph.
Findings: In this paper the existence of (s,d) magic labeling in some cycle related graphs such as a Cycle graph C_(n⊙K_(1,m) )  graph, n -Sunlet graph, Friendship graph Flower graph and wheel graph were found. 
Novelty: The labeling of the vertices and edges is done mathematically, and this leads to the creation of a new labeling known as (s,d) magic labeling.