A multiarrangement, which is a collection of hyperplanes with multiplicities, was introduced by Ziegler for the purpose of solving several problems of free arrangements, e.g., Terao conjecture. There are several interesting studies related to multiarrangements, its logarithmic vector fields and freenss by Solomon, Terao, and Yoshinaga. Especially, Yoshinaga proved that Terao conjecture is closely related to free multiarrangements. In this talk, we give two useful theorems to consider the freeness of multiarrangements, i.e., the addition-deletion theorem and characteristic polynomial. As an application, we classify the free and non-free graphic multiplicity on the Coxeter arrangements of type $A_\ell$. The main part of this talk is joint work with Hiroaki Terao and Max Wakefield.