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 |efₚ^*(0)-efₚ^*(1)|≤ 1 where efₚ^*(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.