Generation of $ \boldsymbol{C_{m} \cdot P_{n}^{l} }$ graphs using $P$ system

Abstract

Graph grammars, used for parsing and generating graphs, provide a useful formalism for describing structural manipulation of multi-dimensional data. Hence graph grammars are used as a synonym for graph rewriting system, especially in the context of languages.  Hyperedge replacement graph grammars, edge replacement graph grammars and node replacement graph grammars are the three types of graph replacement techniques in which hyperedge replacement graph grammar is used in this paper.  $P$ system is a membrane structure consisting of objects and evolution rules in it. The objects can be transformed from on membrane to the other or can dissolve the membrane. In this paper we generate $C_{m} \cdot P_{n}^{l} $ graphs for $m\ge 3,n\ge 2,l\ge 2$ using the $P$ system.