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Prajapati, U. M; Vantiya, A. V
TWMS journal of applied and engineering mathematics, 04/2023, Letnik: 13, Številka: 2Journal Article
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.4S.sub.n), subdivision of double K.sub.4--snake S(D(K.sub.4S.sub.n)), subdivision of alternate K.sub.4--snake S(A(K.sub.4S.sub.n)) of type 1, 2 and 3, and subdivision of double alternate K.sub.4--snake S(DA(K.sub.4S.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.
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