On the balance index set of the chain-sum graphs of cycles - Lee, Sin-Min; Ng, Ho Kuen; Tong, Siu-Ming (Utilitas Mathematica, 2008)
Let G be a graph with vertex set V(G) and edge set E(G), and let A =0, 1. A labeling f: V(G) → A induces a partial edge labeling f*: E(G) → A defined by f*(xy) = f(x) if and only if f(x) = f(y), for each edge xy ∈ E(G). For i ∈ A, let Vf(i) = cardv ∈ V(G): f(v) = i and ef(i) = carde ∈ E(G): f*(e) = i. A labeling f of a graph G is said to be friendly if | Vf(0) - V f(1) | ≤ 1. If | ef(0) - ef(1) | ≤ 1 for a friendly labeling f, then G is said to be balanced. Balancedness of the trees is studied in [2]. The balance Index set of the graph G, BI(G), is defined as | ef(0) - ef(1) : the vertex labeling f is friendly. In this paper we determine balance index sets of some chain sum of graphs.