3-Vertex friendly index sets of operations of two graphs

The process of assigning integer values either to vertices or edges of a graph is known as graph labeling. A mapping f: V(G) ! f0; 1; 2g is called ternary vertex labeling and f (v) represents the vertex label for v. The set FI₃v (G) ¼ f¹¹e_f * (i) ― e_f * ðjÞ¹¹ : f ^* runs over all 3-vertex friendly labeling f for all i; j 2 f0; 1; 2gg is referred as 3-vertex friendly index set. In order to achieve FI₃v (G), number of vertices are partitioned into fV₀; V₁; V₂g such that ¹¹jV_ij ― ¹¹V_j¹¹¹¹ ≤ 1 for all i; j ¼ 0; 1; 2 with i–j and label the edge uv by jf (u) ― f (v)j where f (u); f (v) 2 f0; 1; 2g: A study of 3-vertex friendly index sets of operations of two graphs such as union, join and cartesian product are presented in this paper.