On friendly index sets of spiders

Let g be a graph with vertex set v(g) and edge set e(g),and let a be an abelian group. a 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 ∈ e(g). for i ∈ a,let vf (i) = |{v ∈ v(g): f(v) = i}| and ef (i) = |{e ∈ e(g): f*(e) = i}|. let c(f) = {|ef (i)-ef (j)|: (i,j) ∈ a × a}. a labeling f of a graph g is said to be a-friendly if |vf (i) - vf (j)| ≤ 1 for all (i,j) ∈ a × 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 = z2,the friendly index set of the graph g,fi(g),is defined as {| ef(0) - ef(0)|: the vertex labeling f is z2-friendly}. in this paper,we determined the friendly index sets of many spiders.