An Investigation into Smarandachely Product Cordial Labeling of Rooted Product of cycle to Complete Graph Cn o Km in Communication Network

Abstract- The use of mathematics is quite visible in every area of computer science.Mathematics helps in the design, implementation and analysis of algorithms for scientificand engineering applications. Graph theory is an important area in mathematics. Thispaper explores the use of Smarandachely Product Labeling by labeling the rooted Productof cycle to Complete Graph for the communication Network.In the context of Smarandachely Product Cordial Labeling, this work investigates thelabeling of the Rooted Product of cycle to Complete Graph Cn O Km, where C-{n} timesand K-{m} times. Smarandachely Product Cordial Labeling is defined as a function f: E(G) → {0, 1} that labels the edges of graph G such that each edge uv∈E(G) has theinduced labeling f(u)f(v). | vf (0)-vf (1)| ≥ 2 and |ef (0) - ef (1)| ≥ 2 are the restrictions thatthe labeling must meet. vf (0) and vf (1) stand for the number of vertices with labels 0and 1, respectively, and ef (0) and ef (1) stand for the number of edges with labels 0 and1, respectively. This labeling technique for the given graph product is examined in detailin this study along with its viability and ramifications for graph theory.