K-product cordial labeling of fan graphs

Abstract

Let f be a map from V (G) to {0, 1, ..., k ? 1} where k is an integer, 1 ? k ? |V (G)|. For each edge uv assign the label f(u)f(v)(mod k). f is called a k-product cordial labeling if |vf (i) ? vf (j)| ? 1, and |ef (i) ? ef (j)| ? 1, i, j ? {0, 1, ..., k ? 1}, where vf (x) and ef (x) denote the number of vertices and edges respectively labeled with x (x = 0, 1, ..., k ? 1). In this paper we prove that fan Fn and double fan DFn when k=4 and 5 admit k-product cordial labeling.