On Friendly Index Sets of Broken Wheels with Three Spokes
نویسندگان
چکیده
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 a edge labeling r : E{G) ....... A defined by r(xy) = f(x) + f(y) for each xy E E. For each i E A, let vJ(i) card{v E V(G) : f(v) i} and eJ(i) card{e E E(G) : r(e) i}. Let c(J) {leJ(i) eJ(j)1 : = = (i,j) E A x A}. A labeling f of a graph G is said to be A-friendly if IVJ(i) vJ(j)I::::; I for all (i,j) E A x A. If c(J) is a (0, I)-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 {leJ{O) eJ(I)1 : the vertex labeling f is Z2-friendly}. In [15] the friendly index set of a cycle is completely determined. We consider the friendly index sets of broken wheels with three spokes.
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