On friendly index and product-cordial index sets of Möbius-liked graph

Abstract

Let G be a simple graph with vertex set V(G) and edge set E(G). Let ⟨ℤ2, +,*⟩ be a field with two elements. A vertex labeling f : V(G) → ℤ2 induces two edge labelings f+: E(G) → ℤ2 such that f+ (xy) = f(x) + f(y), whereas f* : E(G) → ℤ2 such that f* (xy) = f(x) f(y), for each edge xy ∈ E(G). For i ϵ ℤ2, let and . A labeling f of a graph G is said to be friendly if |υf (0) −υf (1)|≤ 1. The friendly index set of the graph G, denoted FI(G), is defined as the vertex labeling f is friendly}. This is a generalization of graph cordiality. The corresponding multiplicative version is called the product-cordial index set, denoted PCI(G), defined as the vertex labeling f is friendly}. In this paper, we investigate the friendly index and product-cordial index sets of a family of cubic graphs known as Möbius-liked graph, MG(n) for even n ≥ 4.