3-difference cordial labeling of some cycle related graphs

Abstract

Let <em>G</em> be a (<em>p</em>, <em>q</em>) graph. Let <em>k</em> be an integer with 2 ≤ <em>k</em> ≤ <em>p</em> and <em>f</em> from <em>V</em> (<em>G</em>) to the set {1, 2, . . . , <em>k</em>} be a map. For each edge <em>uv</em>, assign the label |<em>f</em>(<em>u</em>) − <em>f</em>(<em>v</em>)|. The function <em>f</em> is called a <em>k</em>-difference cordial labeling of <em>G</em> if |<em>ν_f</em> (<em>i</em>) − <em>v_f</em> (<em>j</em>)| ≤ 1 and |<em>e_f</em> (0) − <em>e_f</em> (1)| ≤ 1 where <em>v_f</em> (<em>x</em>) denotes the number of vertices labelled with <em>x</em> (<em>x</em> ∈ {1, 2 . . . , <em>k</em>}), <em>e_f</em> (1) and <em>e_f</em> (0) respectively denote the number of edges labelled with 1 and not labelled with 1. A graph with a <em>k</em>-difference cordial labeling is called a <em>k</em>-difference cordial graph. In this paper we investigate the 3-difference cordial labeling of wheel, helms, flower graph, sunflower graph, lotus inside a circle, closed helm, and double wheel.