Graph splicing rules with cycle graph and its complement on complete graphs

Abstract

Graph splicing system is a notion originally used to illustrate the one-dimensional string of DNA splicing in the form of a graph. A graph splicing system is associated with a graph splicing scheme where graph splicing rules are defined. A graph splicing rule restricts the possible cuts to occur on the edges of the initial graph(s) in a graph splicing system. The subgraphs of the initial graph are used in the splicing rules to determine the edges that will be cut from the initial graph. The concept of graph splicing system can be applied on various types of graph, hence generates components of spliced graphs depending on the types of the graph splicing rules used. There is a graph splicing rule called as a cutting rule which can be applied on both linear graphs and circular graphs where the graphs are transformed into Pseudo-Linear Form. However, this cutting rule has limited various possible cuts that can occur on the complete graph. Therefore, in this research, the original concept of graph splicing system is applied on complete graphs as the initial graphs. Also, graph splicing rules involving subgraphs of the initial graphs which are also complete graphs, are considered and applied in the graph splicing system. Furthermore, the generated spliced graphs are obtained through the graph splicing system.