Recent Advancements in Graph Theory

12Total Neighborhood Prime Labeling of Join Graphs

N P Shrimali

Department of Mathematics,Gujarat University,Ahmedabad, Gujarat (INDIA)E-mail: [e-mail]

A K Rathod

Department of Mathematics,Gujarat University,Ahmedabad, Gujarat (INDIA)E-mail: [e-mail]

Let G be a graph with V(G) as the vertex set and E(G) as the edge set. A bijective function f:V(G)∪E(G)→{1,2,3,…,|V(G)∪E(G)|} is said to be a total neighborhood prime labeling, if for each vertex in G having degree greater than 1, the gcd of the labels of its neighborhood vertices is 1 and the gcd of the labels of its induced edges is 1. A graph which admits a total neighborhood prime labeling is called a total neighborhood prime graph. In this chapter, we investigate ...