Prime Labeling of Jahangir Graphs

Abstract

The paper investigates prime labeling of Jahangir graph J_n,m   for n ≥ 2, m ≥ 3 provided that nm is even. We discuss prime labeling of some graph operations viz. Fusion, Switching and Duplication to prove that the Fusion of two vertices v₁ and v_k where k is odd in a Jahangir graph J_n,m results to prime graph provided that the product nm is even and is relatively prime to k. The Fusion of two vertices v_{nm + 1} and v_k for any k in J_{n, m} is prime. The switching of v_k in the cycle C_nm of the Jahangir graph J_n,m  is a prime graph provided that nm+1 is a prime number and the switching of v_nm+1 in J_{n, m} is also a prime graph .Duplicating of v_k, where k is odd integer and nm + 2 is relatively prime to k,k+2 in J_n,m is a prime graph.