A binary vertex coloring (labeling) f : V (G) ! Z2 of a graph G is said to be friendly if the number of vertices labeled 0 is almost the same as the number of vertices labeled 1: This friendly labeling induces an edge labeling f ⁄ : E(G) ! Z2 deflned by f ⁄ (uv) = f(u)f(v) for all uv 2 E(G): Let ef(i) = jfuv 2 E(G) : f ⁄ (uv) = igj be the number of edges of G that are labeled i: Product-cordial index of the labeling f is the number pc(f) = jef(0) i ef(1)j: The product-cordial set of the graph G, denoted by PC(G); is deflned by PC(G) = fpc(f) : f is a friendly labeling of G g: In this paper, we will determine the product-cordial sets of long grids Pm£Pn; introduce a class of fully product-cordial trees and suggest new research directions in this topic.
['Ebrahim Salehi', 'Yaroslav Mukhin']
Product Cordial Sets of Long Grids