LetG be a graph with vertex set V (G) and edge setE(G). A labeling f : V (G) → {0, 1} induces an edge labeling f ∗ : E(G) → {0, 1}, defined by f ∗(xy) = |f (x) − f (y)| for each edge xy ∈ E(G). For i ∈ {0, 1}, let ni(f ) = |{v ∈ V (G) : f (v) = i}| and mi(f )=|{e ∈ E(G) : f ∗(e)= i}|. Let c(f )=|m0(f )−m1(f )|.A labeling f of a graphG is called friendly if |n0(f )−n1(f )| 1. A cordial labeling ...

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...

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) + fey), for each edge xy e E(G). For i e A, let vt<i) = card { v e V(G) : f(v) = i} and er(i) = card ( e e E(G) : f"'(e) = i}. Let c(f) = {Iet<i) etG)1 : (i, j) e A x A}. A labeling f of a graph G is said to be A­ friendly if...

Abstract A binary vertex labeling f : V (G) → Z2 of a graph G is said to be friendly if the number of vertices labeled 0 is almost the same as the number of vertices labeled 1. This friendly labeling induces an edge labeling f∗ : E(G) → Z2 defined by f∗(uv) = f(u)f(v) for all uv ∈ E(G). Let ef (i) = {uv ∈ E(G) : f∗(uv) = i} be the number of edges of G that are labeled i. Productcordial index of...

A binary vertex coloring (labeling) f : V (G) → Z2 of a graph G is said to be friendly if the number of vertices labeled 0 is almost the same as the number of vertices labeled 1. This friendly labeling induces an edge labeling f∗ : E(G) → Z2 defined by f∗(uv) = f(u)f(v) for all uv ∈ E(G). Let ef (i) = |{uv ∈ E(G) : f∗(uv) = i}| be the number of edges of G that are labeled i. Product-cordial ind...

LetG=(V ,E) be a graph, a vertex labeling f : V → Z2 induces an edge labeling f ∗ : E → Z2 defined by f ∗(xy)=f (x)+f (y) for each xy ∈ E. For each i ∈ Z2, define vf (i)=|f−1(i)| and ef (i)=|f ∗−1(i)|. We call f friendly if |vf (1)− vf (0)| 1. The full friendly index set of G is the set of all possible values of ef (1)− ef (0), where f is friendly. In this note, we study the full friendly index...

Let G be a graph with vertex set V (G) and edge set E(G), and f be a 0 − 1 labeling of E(G) so that the absolute difference in the number of edges labeled 1 and 0 is no more than one. Call such a labeling f edge-friendly. We say an edge-friendly labeling induces a partial vertex labeling if vertices which are incident to more edges labeled 1 than 0, are labeled 1, and vertices which are inciden...

For a graph G = (V, E) and a coloring f : V (G) → Z 2 let vf (i) = |f−1(i)|. f is said to be friendly if |vf (1)−vf (0)| ≤ 1. The coloring f : V (G) → Z 2 induces an edge labeling f∗ : E(G) → Z 2 defined by f∗(xy) = f(x) + f(y) ∀xy ∈ E(G), where the summation is done in Z 2. Let ef (i) = |f∗−1(i)|. The friendly index set of the graph G, denoted by FI(G), is defined by FI(G) = {|ef (1)− ef (0)| ...

Let G be a graph with vertex set V and edge set E , and let A be an abelian group. A labeling f : V → A induces an edge labeling f ∗ : E → A defined by f (xy) = f (x) + f (y). For i ∈ A, let v f (i) = card{v ∈ V : f (v) = i} and e f (i) = card{e ∈ E : f (e) = i}. A labeling f is said to be A-friendly if |v f (i)−v f ( j)| ≤ 1 for all (i, j) ∈ A× A, and A-cordial if we also have |e f (i) − e f (...

Let G = (V, E) be a connected simple graph. A labeling f : V → Z2 induces an edge labeling f∗ : E → Z2 defined by f∗(xy) = f(x) + f(y) for each xy ∈ E. For i ∈ Z2, let vf (i) = |f−1(i)| and ef (i) = |f∗−1(i)|. A labeling f is called friendly if |vf (1)− vf (0)| ≤ 1. The full friendly index set of G consists all possible differences between the number of edges labeled by 1 and the number of edge...