4-Prime cordiality of some classes of graphs

Abstract

Let <em>G</em> be a (<em>p</em>, <em>q</em>) graph. Let <em>f</em> : <em>V</em> (<em>G</em>) → {1, 2, . . . , <em>k</em>} be a map. For each edge <em>uv</em>, assign the label gcd (<em>f</em>(<em>u</em>), <em>f</em>(<em>v</em>)). <em>f</em> is called <em>k</em>-prime cordial labeling of <em>G</em> if |<em>v_f</em> (<em>i</em>) − <em>v_f</em> (<em>j</em>)| ≤ 1, <em>i</em>, <em>j</em> ∈ {1, 2, . . . , <em>k</em>} and |<em>e_f</em> (0) − <em>e_f</em> (1)| ≤ 1 where <em>v_f</em> (x) denotes the number of vertices labeled with <em>x</em>, <em>e_f</em> (1) and <em>e_f</em> (0) respectively denote the number of edges labeled with 1 and not labeled with 1. A graph with a<em> k</em>-prime cordial labeling is called a <em>k</em>-prime cordial graph. In this paper we investigate 4- prime cordial labeling behavior of complete graph, book, flower, <em>mC_n</em> and some more graphs.