In this paper, we are studying vertex-magic total labelings (VMTLs) of simple graphs. By now much is known about methods for constructing VMTLs for regular graphs. Here we are studying non-regular graphs. We show how to construct labelings for several families of non-regular graphs, including graphs formed as the disjoint union of two other graphs already possessing VMTLs. We focus on condition...

A vertex-magic total labeling of a graph G(V; E) is a one-to-one map from E ∪V onto the integers {1; 2; : : : ; |E|+ |V |} such that (x) + ∑ (xy); where the sum is over all vertices y adjacent to x, is a constant, independent of the choice of vertex x. In this paper we examine the existence of vertex-magic total labelings of trees and forests. The situation is quite di9erent from the conjecture...

Graph labeling is considered as one of the most interesting areas in graph theory. A for a simple G (numbering or valuation), an association non -negative integers to vertices G  (vertex labeling) edges (edge both them. In this paper we study graceful k- uniform hypertree and define condition corresponding tree be graceful. if minimum difference vertices’ labels each edge dis...

Let G = (V, E) be a simple graph with p vertices and q edges. For connected of diameter d, radio mean labeling is one to mapping f from V(G) N satisfying the condition for every μ, ν ∈ V (G). The span maximum integer that maps vertex G. number G, rmn(G) lowest taken over all labelings In this paper, we analyze some splitting graphs labeling.

An antimagic labeling of a graph withm edges and n vertices is a bijection from the set of edges to the integers 1; . . . ;m such that all n vertex sums are pairwise distinct, where a vertex sum is the sum of labels of all edges incident with that vertex. A graph is called antimagic if it has an antimagic labeling. In [10], Ringel conjectured that every simple connected graph, other than K2, is...

An anti-magic labeling of a finite simple undirected graph with p vertices and q edges is a bijection from the set of edges to the set of integers {1, 2, . . . , q} such that the vertex sums are pairwise distinct, where the vertex sum at one vertex is the sum of labels of all edges incident to such vertex. A graph is called anti-magic if it admits an anti-magic labeling. Hartsfield and Ringel c...

Let G = (V, E) be a simple graph. A vertex labeling f : V → {0, 1} induces a partial edge labeling f ∗ : E → {0, 1} defined by f ∗(uv) = f(u) 84 KWONG, LEE, LO, SU AND WANG if and only if f(u) = f(v). For i = 0, 1, let vf(i) = |{v ∈ V : f(v) = i}|, and ef (i) = |{e ∈ E : f ∗(e) = i}|. A graph G is uniformly balanced if |ef (0)−ef (1)| ≤ 1 for any vertex labeling f that satisfies |vf(0)−vf (1)| ...