Freund[4] introduced the graph Splicing Scheme for the DNA molecules. Oassow and Mintrana [3] studies the Hyperedge replacement graph and examine the notation of self Cross-over system. K.G Subramanian et al. [13] examines the relationships between graph splicing Languages of Freund and Hyperedge replacement graph Languages. In this paper we propose LGSCOG (Line graphs of Self-Cross over Graphs) for the self Cross-over systems and get homomorphism properties between Line Graphs in graph splicing languages. We proved the relations between the Graphs when the numbers of splicing language have the same number of molecules.
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