Full friendly index sets of mCn

Let G be a connected simple graph with vertex set V(G) and edge set E(G). A binary vertex labeling f: V(G) -> DOUBLE-STRUCK CAPITAL Z(2), 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) -> DOUBLE-STRUCK CAPITAL Z(2), defined by f*(xy) = f(x) + f(y) for each xy is an element of E(G). Let e(f*)(i) = |{e is an element of E(G): f*(e) = i}|. The full friendly index set of G, denoted by FFI(G), is the set {e(f)*(1) - e(f)*(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 P-2 x P-n.

Automated summary

This paper investigates the full friendly index set of a family of graphs, exploring the relationship between friendly vertex labeling and edge labeling functions.