  Design patterns being applied more and more to solve the software engineering
difficulties in the object oriented software design procedures. So, the design
pattern detection is widely used by software industries. Currently, many
solutions presented to detect the design pattern in the system design. In this
paper, we will propose a new one which first; we will use the graph
implementation to implement both the system design UML diagram and the design
pattern UML diagram. Second, we will implement the edges for each one of the
both two graphs in a set of 4-tuple elements. Then, we will apply a new inexact
graph isomorphic algorithm to detect the design pattern in the system design.
