A total k-labeling is a function fe from the edge set to {1, 2, . , ke} and fv vertex {0, 4, 2kv}, where k = max{ke, 2kv}. distance irregular reflexive of graph G k-labeling, if for every two different vertices u 0 G, w(u) 6= w(u ), Σui∈N(u)fv(ui) + Σuv∈E(G)fe(uv). The minimum which has k-labelling called strength denoted by Dref (G). In this paper, we determine exact value some connected graph...

Let G = (V;E) be a graph. A total labeling ψ : V ⋃ E → {1, 2, ....k} is called totally irregular k-labeling of if every two distinct vertices u and v in (G) satisfy wt(u) ≠wt(v); edges u1u2 v1v2 E(G) wt(u1u2) ≠ wt(v1v2); where (u) + ∑uv∊E(G) ψ(uv) ψ(u1) ψ(u1u2) ψ(u2): The minimum k for which graph has the irregularity strength G, denoted by ts(G): In this paper, we determine exact value cubic g...

A graph with p vertices and q edges is said to have an even vertex odd mean labeling if there exists an injective function f:V(G){0, 2, 4, ... 2q-2,2q} such that the induced map f*: E(G) {1, 3, 5, ... 2q-1} defined by f*(uv)=     f u f v 2  is a bijection. A graph that admits an even vertex odd mean labeling is called an even vertex odd mean graph. In this paper we pay our attention to p...

As a standard notation, assume that G = G(V,E) is a finite, simple and undirected graph with p vertices and q edges. A labeling of a graph is any mapping that sends some set of graph elements to a set of numbers (usually positive integers). If the domain is the vertex-set or the edge-set, the labelings are called respectively vertex-labelings or edge-labelings. If the domain is V ∪E then we cal...

A universal labeling of a graph G is a labeling of the edge set in G such that in every orientation l of G for every two adjacent vertices v and u, the sum of incoming edges of v and u in the oriented graph are different from each other. The universal labeling number of a graph G is the minimum number k such that G has universal labeling from {1, 2, . . . , k} denoted it by −→ χu(G). We have 2∆...

A labeling of a graph G is a bijection from E(G) to the set {1, 2, . . . , |E(G)|}. A labeling is antimagic if for any distinct vertices u and v, the sum of the labels on edges incident to u is different from the sum of the labels on edges incident to v. We say a graph is antimagic if it has an antimagic labeling. In 1990, Ringel conjectured that every connected graph other than K2 is antimagic...

The concept of fuzzy magic labeling is introduced.Fuzzy magic labeling for some graphs like path, cycle and star graph are defined. It is proved that, every fuzzy magic graph is a fuzzy labeling graph, but the converse is not true. And we show that the removal of a fuzzy bridge from a fuzzy magic graph G, such that G* is a cycle with odd number of nodes is a fuzzy magic graph.And also some prop...

Let G be a simple graph of n order. An edge labeling such that the weights all vertex are different and elements set modulo n, called modular irregular labeling. The irregularity strength is minimum positive integer k have If none, then we infinity. In this article, determine complete graphs.

Let G be a graph of order n and size m. A labeling of G is a bijective mapping θ : V(G) → {1, 2, . . . , n}, and we call Θ(G) the set of all labelings of G. For any graph G and any labeling θ ∈ Θ(G), let SL(G, θ) = ∑ e∈E(G)min{θ(u) : u ∈ e}. In this paper, we consider the S-Labeling problem, defined as follows: Given a graph G, find a labeling θ ∈ Θ(G) that minimizes SL(G, θ). The S-Labeling pr...

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 ...