(untitled) (European Journal of Pure and Applied Mathematics, 2025)
In this paper, we introduce a new labeling namely `edge k-product cordial labeling’ as follows: For a graph G=(V(G), E(G)) having no isolated vertex, an edge labeling f:E(G)→ 0,1,...,k-1 brace, where k>1 is an integer, is said to be an edge k-product cordial labeling if it induces a vertex labeling f^:V(G)→ 0,1,...,k-1 brace defined by f^(v)=_uvE(G) f(uv)(mod k) satisfies | e_f(i)-e_f(j) | ≤ 1 and |v_f^(i)-v_f^(j) | ≤ 1 for i,j 0,1,..., k-1 brace, where e_f(i) and v_f^(i) denote the number of edges and vertices respectively having a label i (i=0,1,...,k-1). Further, we study the edge k-product cordial behavior of star, bistar, shadow and splitting graph of star, path union of star, bistar and cycle graphs.