A 3-equitable prime cordial labeling of a graph G with vertex set V is a bijection f from V to {1, 2, ..., |V |} such that if an edge uv is assigned the label 1 if gcd(f(u), f(v)) = 1 and gcd(f(u) + f(v), f(u)−f(v)) = 1, the label 2 if gcd(f(u), f(v)) = 1 and gcd(f(u) + f(v), f(u)− f(v)) = 2 and 0 otherwise, then the number of edges labeled with i and the number of edges labeled with j differ b...

Hovey [Discrete Math. 93 (1991), 183–194] introduced simultaneous generalizations of harmonious and cordial labellings. He defines a graph G of vertex set V (G) and edge set E(G) to be k-cordial if there is a vertex labelling f from V (G) to Zk, the group of integers modulo k, so that when each edge xy is assigned the label (f(x) + f(y)) (mod k), the number of vertices (respectively, edges) lab...

A divisor cordial labeling of a graph G with vertex set V vertex G is a bijection f from V to {1, 2, 3, . . . |V|} such that an edge uv is assigned the label 1 if f(u) divides f(v) or f(v)divides f(u) and 0 otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. If a graph has a divisor cordial labeling, then it is called divisor cordial gr...

Abstract. A sum divisor cordial labeling of a graph G with vertex set V is a bijection f from V to {1,2,...,| ( ) |} V G such that each edge uv assigned the label 1 if 2 divides ( ) ( ) f u f v + and 0 otherwise. Further, the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. A graph with a sum divisor cordial labeling is called a sum divisor cordial grap...

Received: December 16, 2010 Accepted: December 31, 2010 doi:10.5539/jmr.v3n2p206 Abstract In this paper we investigate product cordial labeling for some new graphs. We prove that the friendship graph, cycle with one chord (except when n is even and the chord joining the vertices at diameter distance), cycle with twin chords (except when n is even and one of the chord joining the vertices at dia...

A graph is said to be cordial if it has 0 - 1 labeling which satisfies particular conditions. In this paper, we construct the corona between paths and second power of fan graphs explain necessary sufficient conditions for construction cordial.

In this paper we work on the Bloom Torus graph by satisfying condition of Smarandachely product cordial labeling. labeling is such a with induced

vspace{0.2cm} Let $G$ be a graph and $f:V(G)rightarrow {1,2,3,.....left|V(G)right|}$ be a bijection. Let $p_{uv}=f(u)f(v)$ and\ $ d_{uv}= begin{cases} left[frac{f(u)}{f(v)}right] ~~if~~ f(u) geq f(v)\ \ left[frac{f(v)}{f(u)}right] ~~if~~ f(v) geq f(u)\ end{cases} $\ for all edge $uv in E(G)$. For each edge $uv$ assign the label $1$ if $gcd (p_{u...

Hovey introduced $A$-cordial labelings as a generalization of cordial and harmonious \cite{Hovey}. If $A$ is an Abelian group, then labeling $f \colon V (G) \rightarrow A$ the vertices some graph $G$ induces edge on $G$; $uv$ receives label (u) + f (v)$. A if there vertex-labeling such that (1) vertex classes differ in size by at most one (2) induced one. Patrias Pechenik studied larger class f...