International Journal of Computer Applications (0975 – 8887) Volume 49– No.8, July 2012 18 Splicing Operation on Graphs Meena Parvathy Sankar Department of Mathematics SRM University Kattankulathur − 603203 N. Gnanamalar David Department of Mathematics Madras Christian College Tambaram, Chennai − 600059 D. Gnanaraj Thomas Department of Mathematics Madras Christian College Tambaram, Chennai − 600059 ABSTRACT In this paper, we introduce the splicing operation on graph P system with the feature of conditional communication. We use the notions of Fruend graph splicing and generate the string graph languages. We study the generative power of the splicing graph P system with conditional communication with the other classes of string graph languages and give comparison results of the languages generated by the system. Keywords Graph splicing, Conditional communication, Splicing graph P system. 1. INTRODUCTION The splicing systems were introduced by Head to investigate the power of computing with DNA. The recent development in this field is the generalization of the splicing concept to graphs by Rudolf Freund [2, 6]. It is an accurate model of a system consisting of biochemical units and the interactions between them. The structure and the functioning of a biological cell were inspired by a class of distributed parallel computing devices called the P system [4, 5]. In this paper, we define graph splicing P system with the feature of conditional communication. 2. PRELIMINARIES We recall the notions of graph splicing system in this section [1, 2]. 2.1Graph Splicing System A graph splicing system σ is represented by a pair ( , P) where is an alphabet of the system and P is a set of graph splicing rules which is finite and is of the form ((h[1], E′[1]), …, (h[k], E′[k]); E) where k ≥ 1 and for all i with 1 ≤ i ≤ k, h[i] = (V[i], E[i], L[i]), E′[i] E[i], The set of cut edges is given by E′[i] , V[i] is called the node sets and they are mutually disjoint and E must obey the following rules: 1. Each edge (n, m) E′[i] is divided into two parts, that is, the start part (n, m] and the end part [n, m). 2. The elements of E are of the form ((n, m], [n′, m′)), where (n, m) and (n′, m′) are edges from ′[i]. 3. Every element from [i]} E m) m)/(n, [n, m], {(n, should appear exactly once in a pair of E. 2.2Graph Splicing Step Let the graph splicing system be represented by σ = (Σ, P) and let the rule in P is given by p = ((h[1], E'[1]),…, (h[k], E'[k]); E) . Then the set R of graphs derives a set S of graphs through the splicing rule p if there exists graphs g[1], g[2], …, g[k] R and graphs g'[1], g'[2], …, g'[m] S such that, h[i] is an induced sub graph of g[i] for all i with 1 ≤ i ≤ k,. From g[1], g[2], …, g[k] we delete all the edges corresponding to edges in ′[i] but add each edge corresponding to the edge ((n, m], [n', m')) E, which yields the uniquely determined union of m connected graphs g'[1], g'[2], …, g'[m]. In this graph splicing, we use implicitly the multisets of graphs; g[j] may be another copy of g[i]. The idea of graph splicing rule is to cut the various edges in some graphs and rejoin the edges in another fashion. 2.3 Extended Graph Splicing System The graph splicing system is represented by = (Σ, P) and I be a finite set of graphs, called the set of axioms. The extended graph splicing step is given by quadruple (N, T, P, I) where N and T are disjoint sets of nonterminals and terminals respectively, and N T = . (I) is the minimal set of graphs obtain by applying some splicing rules to some subset of I. (I) is defined iteratively as (I)); (I) is defined to be I. We also define (I) = . The graph language L(F) generated by an extended graph splicing system F = (N, T, P, I ) is L(F) = {g = (V, E, F) (I) / F(n) T, . 3. SPLICING GRAPH P SYSTEM WITH CONDITIONAL COMMUNICATION In this section, we define a splicing graph P system and examine its generative power by adding the feature conditional communication. 3.1 Definition A splicing graph P system with conditional communication (SGPCC) is a construct ) , ( ), , , ( ),..., , , ( , ,..., , , , , ( 1 1 1 2 1 d n F P R F P R A A A T V n n n n where V is a finite set of nonterminal and terminal symbols; T is a set of terminal symbols available in V; μ is membrane structure with n membranes and depth d (maximum no of membranes in the nesting of membranes in the whole system); each * V A i , i {1, 2, ..., n} are the finite languages associated with the compartments 1, 2, …, n of µ; R i is a finite set of graph rules associated with the region i, i = 1, 2, …, n which is of the form (V, P) where V is an alphabet and P is a finite set of graph splicing rules as given in the definition of graph splicing. The rules are used in the regions in parallelism mode as follows: A rewriting step with parallelism involves substitution of all occurrences of one edge according to a rule that can be applied to that edge. P i and F i are permitting and forbidding