SD-prime cordial labeling of subdivision K₄−snake and related graphs

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 fʹ be the induced edge labeling, induced by the vertex labeling f, defined as fʹ: E(G) → {0, 1} such that for any edge uv in E(G), fʹ(uv) = 1 if gcd(S, D) = 1, and fʹ(uv) = 0 otherwise. Let e(fʹ) (0) and e(fʹ) (1) be the number of edges labeled with 0 and 1 respectively. f is SD-prime cordial labeling if |e(fʹ) (0) − e(fʹ) (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(K₄Sn), subdivision of double K₄−snake S(D(K₄Sn)), subdivision of alternate K₄−snake S(A(K₄Sn)) of type 1, 2 and 3, and subdivision of double alternate K₄− snake S(DA(K₄Sn)) of type 1, 2 and 3.Publisher's Versio