The string splicing was introduced by Tom Head which stands as an abstract model for the DNA recombination under the influence of restriction enzymes. The complex chemical process of three dimensional molecules in three dimensional space can be modeled using graphs. The graph splicing systems which were studied so far, can only be applied to a particular type of graphs which could be interpreted as linear or circular graphs. In this paper, we take a different and a novel approach to splice two graphs and introduce a splicing system for graphs that can be applied to all types of graphs. Splicing two graphs can be thought of as a new operation, among the graphs, that generates many new graphs from the given two graphs. Taking a different line of thinking, some of the graph theoretical results of the splicing are studied. It is proved that the splicing operation among graphs is reversible and the membership problem of splicing graph language is studied.
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