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One interesting topic in algebra and graph theory is a graph representation of a group, especially the representation of a group using a non-coprime graph. In this paper, we describe the non-coprime graph of integers modulo group and its subgroups, for is a prime power or is a product of two distinct primes.doi:10.14710/jfma.v3i2.8713 fatcat:uusgyxvmyrdbfo5zvigmmmnm3y