On Legendre Cordial Labeling of Some Graphs Under Graph Opearations

For a simple connected graph G of order n, a bijective function f: V (G) \1, 2, , n\ is said to be a Legendre cordial labeling modulo p, where p is an odd prime, if the induced function fₚ^*: E (G) \0, 1\, defined by fₚ^* (uv) =0 whenever (f (u) +f (v) /p) =-1 or f (u) +f (v) 0 (mod p), and fₚ^* (uv) =1 whenever (f (u) +f (v) /p) =1, satisfies the condition |e₅䂹^* (0) -e₅䂹^* (1) | 1 where e₅䂹^* (i) is the number of edges with label i (i=0, 1). This paper investigates the Legendre cordial labeling of graphs obtained through various operations: join, corona, lexicographic product, cartesian product, tensor product, and strong product.