Full friendly index sets of mCn

摘要

Let G be a connected simple graph with vertex set V(G) and edge set E(G). A binary vertex labeling f: V(G) → ℤ2, is said to be friendly if the number of vertices with different labels differs by at most one. Each vertex friendly labeling f induces an edge labeling f*: E(G) → ℤ2, defined by f*(xy) = f(x) + f(y) for each xy ∈ E(G). Let ef*(i) = |{e ∈ E(G): f*(e) = i}|. The full friendly index set of G, denoted by FFI(G), is the set {ef*(1) − ef*(0): f is friendly}. In this paper, we determine the full friendly index set of a family of cycle union graphs which are edge subdivisions of P2 × Pn.