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Prime labeling is an assignment of integers to the vertices which are relatively prime. The theory behind the graph labeling were introduced by Rosa in the 1960s. A huge number of prime labeling research works have been discovered for various types of graphs today after undergoing different methods. In this work, the prime labeling method has been introduced for the circular ladder graph ?CL?_n with 2n vertices when n is an even. The graph obtained by using cartesian product of C_n with n vertices and path graph of the form P_2 is called circular ladder graph and is denoted by ?CL?_n (i.e C_n×P_2=?CL?_n). We proved that ?CL?_n is a prime graph for two special cases when n is an even integer and n+1 is prime, and when n is an even integer and 2n+1 is prime. In addition, the cyclic vertex labeling method in the clockwise direction and anti-clockwise direction have been introduced. Moreover, proofs of the two theorems related to the above two cases are given. We used the theorem on ladder graphs in the work by A. H. Berliner et al. to prove these results.
Circular Ladder Graph, Graph Labeling, Prime Labeling
A.P. Batuwita , M.D.M.C.P. Weerarathna , G.W.M.M.K. Dheerasinghe "Prime Labeling of Circular Ladder Graph (CLn)" Iconic Research And Engineering Journals Volume 4 Issue 10 2021 Page 192-195
A.P. Batuwita , M.D.M.C.P. Weerarathna , G.W.M.M.K. Dheerasinghe "Prime Labeling of Circular Ladder Graph (CLn)" Iconic Research And Engineering Journals, 4(10)