The correct answer is $\boxed{\text{C}}$.
An m-bit parallel adder is a circuit that adds two m-bit numbers together. It can be constructed using m full adders. A full adder is a circuit that adds two bits together and produces a sum bit and a carry bit. To add two m-bit numbers, we need to add each pair of bits, starting from the least significant bit (LSB) and working our way up to the most significant bit (MSB). For each pair of bits, we need a full adder. Therefore, we need m full adders to construct an m-bit parallel adder.
Option A is incorrect because it is the number of half adders required to construct an m-bit parallel adder. A half adder is a circuit that adds two bits together and produces a sum bit. To add two m-bit numbers, we need to add each pair of bits, starting from the LSB and working our way up to the MSB. For each pair of bits, we need a half adder. Therefore, we need $\frac{m}{2}$ half adders to construct an m-bit parallel adder.
Option B is incorrect because it is the number of full adders required to construct an (m-1)-bit parallel adder. To add two (m-1)-bit numbers, we need to add each pair of bits, starting from the LSB and working our way up to the MSB. For each pair of bits, we need a full adder. Therefore, we need $(m-1)$ full adders to construct an (m-1)-bit parallel adder.
Option D is incorrect because it is the number of full adders required to construct an (m+1)-bit parallel adder. To add two (m+1)-bit numbers, we need to add each pair of bits, starting from the LSB and working our way up to the MSB. For each pair of bits, we need a full adder. Therefore, we need $(m+1)$ full adders to construct an (m+1)-bit parallel adder.
Option E is incorrect because it is not a valid option.