Group S3 Cordial Remainder Labeling of n-Copies of Path and Cycle Graphs

ABSTRACT
Let 𝐺 = (𝑉(𝐺),𝐸(𝐺)) be a graph. Let ℎ:𝑉(𝐺)→𝑆3 be a function. For each edge 𝑥𝑦 assign the label r where r is the remainder when 0(ℎ(𝑥)) is divided by 𝑜(ℎ(𝑦)) or 𝑜(ℎ(𝑦)) is divided by 𝑜(ℎ(𝑥)) according as 𝑜(ℎ(𝑥)) ≥ 𝑜(ℎ(𝑦)) or 𝑜(ℎ(𝑦)) ≥ 𝑜(ℎ(𝑥)). The function h is called a group 𝑆3 cordial remainder labeling of 𝐺 if |𝑣ℎ(𝑖) – 𝑣ℎ(𝑗)| ≤ 1 and |𝑒ℎ(1) – 𝑒ℎ(0)| ≤ 1, where 𝑣ℎ(𝑗) denotes the number of vertices labeled with j and 𝑣ℎ(𝑖) denotes the number of edges labeled with 𝑖 (𝑖 = 0,1). A graph 𝐺 which admits a group 𝑆3 cordial remainder labeling is called a group 𝑆3 cordial remainder labeling is called a group 𝑆3 cordial remainder graph. In this paper, we

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