SD-PRIME CORDIAL LABELING OF SUBDIVISION K4−SNAKE AND RELATED GRAPHS

SD-PRIME CORDIAL LABELING OF SUBDIVISION K4−SNAKE AND RELATED GRAPHS

U. M. Prajapati, A. V. Vantiya

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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 f0 be the induced edge labeling, induced by the vertex labeling f, defined as f0 : E(G) ! {0, 1} such that for any edge uv in E(G), f0(uv) = 1 if gcd(S,D) = 1, and f0(uv) = 0 otherwise. Let ef0 (0) and ef0 (1) be the number of edges labeled with 0 and 1 respectively. f is SD-prime cordial labeling if |ef0 (0) − ef0 (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.

Keywords

SD-prime cordial graph, Subdivision of K4−Snake, Subdivision of Alternate K4−Snake, Subdivision of Double K4−Snake, Subdivision of Double Alternate K4−Snake, m−Complete Snake.