On friendly index sets of total graphs of trees

Let G be a graph with vertex set V(G) and edge set E(G), and let A be an abelian group. A vertex labeling f: V(G) -> A induces an edge labeling f* : E(G) -> A defined by f*(xy) = f(x) + f(y), for each edge Xy epsilon E(G). For i epsilon A, let v(f)(i) = card {v epsilon V(G) : f(v) = i} and e(f)(i) = card {e epsilon E(G) : f*(e) = i}. Let c(f) = {vertical bar e(f)(i) - e(f)(i)vertical bar : (i, j) epsilon A x A}. A labeling f of a graph G is said to be A-friendly if vertical bar v(f)(i) - v(f)(j)vertical bar <= 1 for all (i, j) epsilon A x A. If c(f) is a (0, 1)-matrix for an A-friendly labeling f, then f is said to be A-cordial. When A = Z(2), the friendly index set of the graph G, FI(G), is defined as {vertical bar e(f)(0) - e(f) (1)vertical bar : the vertex labeling f is Z(2)-friendly}. In this paper the friendly index sets of the total graphs of some trees are completely determined.