SD-PRIME CORDIAL LABELING OF SUBDIVISION [K.sub.4]--SNAKE AND RELATED GRAPHS

Let f : V(G) [right arrow] {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) [right arrow] {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.sub.f']/(0) and [e.sub.f']/(1) be the number of edges labeled with 0 and 1 respectively. f is SD-prime cordial labeling if |[e.sub.f']/(0) - [e.sub.f']/(1)| [less than or equal to] 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 [K.sub.4]--snake S([K.sub.4][S.sub.n]), subdivision of double [K.sub.4]--snake S(D([K.sub.4][S.sub.n])), subdivision of alternate [K.sub.4]--snake S(A([K.sub.4][S.sub.n])) of type 1, 2 and 3, and subdivision of double alternate [K.sub.4]--snake S(DA([K.sub.4][S.sub.n])) of type 1, 2 and 3. Keywords: SD-prime cordial graph, Subdivision of [K.sub.4]--Snake, Subdivision of Alternate [K.sub.4]--Snake, Subdivision of Double [K.sub.4]--Snake, Subdivision of Double Alternate [K.sub.4]--Snake, m--Complete Snake. AMS Subject Classification: 05C78.