  Quantum walks with memory(QWM) are a type of modified quantum walks that
record the walker's latest path. As we know, only two kinds of QWM are
presented up to now. It is desired to design more QWM for research, so that we
can explore the potential of QWM. In this work, through presenting the
one-to-one correspondence between QWM on a regular graph and quantum walks
without memory(QWoM) on line digraph of the regular graph, we construct a
generic model of QWM on regular graphs. This construction gives a general
scheme for building all possible standard QWM on regular graphs and makes it
possible to study properties of different kinds of QWM. Here, by taking the
simplest example which is QWM with 1 memory on the line, we analyze some
properties of QWM, such as variance, occupancy rate and localization.
