Edge k-Product Cordial Labeling of Trees

The concepts of k-product cordial labeling and edge product cordial labeling were introduced in 2012 and further explored by various researchers. Building on these ideas, we define a new concept called ‘edge k-product cordial labeling’ as follows: For a graph G=(V(G),E(G)), which does not have isolated vertices, an edge labeling f:E(G)→0,1,…,k−1, where k≥2 is an integer, is said to be an edge k-product cordial labeling of G if it induces a vertex labeling f*:V(G)→0,1,…,k−1 defined by f*(v)=∏uv∈E(G)f(uv)(modk), which satisfies ef(i)−ef(j)≤1 and vf*(i)−vf*(j)≤1 for i,j∈0,1,…,k−1, where ef(i) and vf*(i) denote the number of edges and vertices, respectively, having label i for i=0,1,…,k−1. In this paper, we study the edge k-product cordial behavior of trees, a comet, and a double comet.