SD-prime cordial labeling of subdivision K??snake and related graphs

Abstract

Let f : V (G) ? {1, 2, . . . , |V (G)|} be a bijection, and let us denote S = f(u)+f(v) and D = |f(u)?f(v)| for every edge uv in E(G). Let f? be the induced edge labeling, induced by the vertex labeling f, defined as f?: E(G) ? {0, 1} such that for any edge uv in E(G), f?(uv) = 1 if gcd(S, D) = 1, and f?(uv) = 0 otherwise. Let e(f?) (0) and e(f?) (1) be the number of edges labeled with 0 and 1 respectively. f is SD-prime cordial labeling if |e(f?) (0) ? e(f?) (1)| ? 1 and G is SD-prime cordial graph if it admits SD-prime cordial labeling. In this paper, we have discussed the SD-prime cordial labeling of subdivision of K4?snake S(K?Sn), subdivision of double K??snake S(D(K?Sn)), subdivision of alternate K??snake S(A(K?Sn)) of type 1, 2 and 3, and subdivision of double alternate K?? snake S(DA(K?Sn)) of type 1, 2 and 3.