Let G be a finite graph with p vertices and q edges. A vertex magic total labeling is a bijection f from     G E G V  to the consecutive integers 1, 2, ..., p+q with the property that for every   G V u ,       k uv f u f u N v     for some constant k. Such a labeling is E-super if     q G E f , , 2 , 1 :   . A graph G is called E-super vertex magic if it admits an E-supe...

Abstract Let $(z_k)$ be a sequence of distinct points in the unit disc $\mathbb {D}$ without limit there. We are looking for function $a(z)$ analytic and such that possesses solution having zeros precisely at $z_k$ , resulting has ‘minimal’ growth. focus on case non-separated sequences terms pseudohyperbolic distance when coefficient is zero order, but $\sup _{z\in {\mathbb D}}(1-|z|)^p|a(z)| =...

A graph is called degree-magic if it admits a labelling of the edges by integers 1, 2, . . . , |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal to 1+|E(G)| 2 deg(v). Degree-magic graphs extend supermagic regular graphs. In this paper we characterize complete tripartite degree-magic graphs.

For any h ∈ Z, a graph G = (V, E) is said to be h-magic if there exists a labeling l : E(G) → Zh−{0} such that the induced vertex set labeling l : V (G) → Zh defined by l(v) = ∑ uv∈E(G) l(uv) is a constant map. For a given graph G, the set of all h ∈ Z+ for which G is h-magic is called the integermagic spectrum of G and is denoted by IM (G). In this paper, we will determine the integer-magic sp...

A vertex magic total labeling on a graph with v vertices and e edges is a one to one map taking the vertices and edges onto the integers with the property that the sum of the label on the vertex and the labels of its incident edges is a constant, independent of the choice of the vertex. A graph with vertex magic total labeling with two constants or is called a vertex bimagic total labeling. The...

A graph G of order n and size m is edge-magic if there is a bijection l : V (G) ∪E(G) → [n+m] such that all sums l(a) + l(b) + l(ab), ab ∈ E(G), are the same. We present new lower and upper bounds on M(n), the maximum size of an edge-magic graph of order n, being the first to show an upper bound of the form M(n) ≤ (1 − ǫ) ( n 2 ) . Concrete estimates for ǫ can be obtained by knowing s(k, n), th...

Let G = (V,E) be a graph of order n. A distance magic labeling of G is a bijection l : V → {1, . . . , n} for which there exists a positive integer k such that ∑ x∈N(v) l(x) = k for all v ∈ V , where N(v) is the neighborhood of v. We introduce a natural subclass of distance magic graphs. For this class we show that it is closed for the direct product with regular graphs and closed as a second f...

A graph is called magic (supermagic) if it admits a labelling of the edges by pairwise different (and consecutive) positive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In the paper we prove that any balanced bipartite graph with minimum degree greater than |V (G)|/4 ≥ 2 is magic. A similar result is presented for supermag...

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...