Final answer:
The chromosomal inversion that does not include the centromere is called a paracentric inversion, which affects only one arm of a chromosome without altering its lengths.
Step-by-step explanation:
A chromosomal inversion that does not include the centromere is known as a paracentric inversion. This type of inversion only involves one arm of the chromosome, as opposed to pericentric inversions which include the centromere and can alter the relative lengths of the chromosome arms. A paracentric inversion does not involve the central part of the chromosome and therefore does not change the arm lengths.