  The class of UMP algebras arises in several classification problems in the
context of derived categories of finite-dimensional algebras. In this paper we
define the class of UMP algebras and develop algebraic combinatorics tools in
order to present a characterization of this class of algebras which are locally
monomial (see Definition 4.1) and special multiserial algebras. Among other
things, we describe the ramifications graph of symmetric special biserial
algebras and we classify which of them are UMP algebras in terms of their bound
quivers and their associated Brauer graphs.
