Quotient square sum cordial labeling

Abstract

Let G = (V, E) be a simple graph and ϕ: V {1, 2, … | V |} be a bijection, for each edge uv assigned the label 1 if (Formula Presented) is odd and 0 if (Formula Presented) is even. ϕ is called quotient square sum cordial labeling if |eϕ(0) − eϕ(1)| ≤ 1, where eϕ(0) and eϕ(1) denote the number of edges labeled with 0 and labeled with 1 respectively. A graph which admits a quotient square sum cordial labeling is called quotient square sum cordial graph. In this paper path Pn, cycle Cn, star K1,n, friendship graph Fn, bistar Bn,n, C4 ∪ Pn,Km,2 and Km,2 ∪ Pn are shown to be quotient square sum cordial labeling.