Uniformly cordial graphs

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 ofG is a friendly labeling f for which c(f ) 1.A graphG is a uniformly cordial graph if every friendly labeling of G is cordial. It is shown that a connected graph G of order n 2 is uniformly cordial if and only if n = 3 and G = K3, or n is even and G=K1,n−1. © 2006 Elsevier B.V. All rights reserved.