Prime Labeling of Jahangir Graphs

Abstract

The paper investigates prime labeling of Jahangir graph Jn,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 vk where k is odd in a Jahangir graph Jn,m results to prime graph provided that the product nm is even and is relatively prime to k. The Fusion of two vertices vnm + 1 and vk for any k in Jn, m is prime. The switching of vk in the cycle Cnm of the Jahangir graph Jn,m is a prime graph provided that nm+1 is a prime number and the switching of vnm+1 in Jn, m is also a prime graph .Duplicating of vk, where k is odd integer and nm + 2 is relatively prime to k,k+2 in Jn,m is a prime graph.

The Vertex Prime Valuation for Jahangir and Theta Graphs

“…A graph that admits a vertex prime labeling is called a vertex prime graph. A description on prime labeling of Jahangir graph can be found in [1]. Throughout this paper, we consider finite simple undirected graphs.…”

Pelabelan Prima pada Graf Simpul Semi Total dari Graf Sikat

“…Beberapa kelas graf yang merupakan graf prima diantaranya graf gurita (Edward, Samuel, & Kalaivani, 2016), graf Lilly (Samuel & Kalaivani, 2018a), graf drum (Samuel & Kalaivani, 2018) dan graf Jahangir (Lakshmi et al, 2018). Graf prima juga dapat diperoleh dari hasil operasi antar graf-graf prima (Prajapati & Gajjar, 2014).…”