A graph G is called edge-magic if there exists a bijective function φ : V (G)∪E(G) → {1, 2,. .. , |V (G)|+ |E(G)|} such that φ(x)+φ(xy)+φ(y) is a constant c(φ) for every edge xy ∈ E(G); here c(φ) is called the valence of φ. A graph G is said to be super edge-magic if φ(V (G)) = {1, 2,. .. , |V (G)|}. The super edge-magic deficiency, denoted by μ s (G), is the minimum nonnegative integer n such ...

A (p, q) graph G is called edge-magic if there exists a bijective function f : V (G) ∪ E(G) → {1, 2, . . . , p + q} such that f(u) + f(v) + f(uv) is constant for any edge uv of G. Moreover, G is said to be super edgemagic if f(V (G)) = {1, 2, . . . , p}. Every super edge-magic (p, q) graph is harmonious, sequential and felicitous whenever it is a tree or satisfies q ≥ p. In this paper, we prove...

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

ON SUPER EDGE-MAGIC TOTAL LABELING OF REFLEXIVE W-TREES Muhammad Imran, Mehar Ali Malik, M. Yasir Hayat Malik Department of Mathematics, School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Islamabad, Pakistan. E-mail: {imrandhab, alies.camp, yasirmalikawan}@gmail.com Mathematics Subject Classification: 05C78 ABSTRACT. Kotzig and Rosa [17] defined a magic lab...

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...

The study of graph labeling has focussed on finding classes of graphs which admits a particular type of labeling. In this paper we consider a particular class of graph which admits a vertex magic total labeling. The class we considered here is the class of complete graphs, Kn . A vertex magic labeling of a graph is a bijection which maps the vertices V and edges E to the integers from 1, 2, 3, ...

We investigate the existence of edge-magic labellings of countably infinite graphs by abelian groups. We show for that for a large class of abelian groups, including the integers Z, there is such a labelling whenever the graph has an infinite set of disjoint edges. A graph without an infinite set of disjoint edges must be some subgraph of H + I, where H is some finite graph and I is a countable...

A group distance magic labeling or aG-distance magic labeling of a graph G = (V, E) with |V | = n is a bijection f from V to an Abelian group G of order n such that the weight w(x) = ∑y∈NG (x) f (y) of every vertex x ∈ V is equal to the same element μ ∈ G, called the magic constant. In this paper we will show that if G is a graph of order n = 2p(2k + 1) for some natural numbers p, k such that d...

Various graph labelings that generalize the idea of a magic square have been discussed. In particular a magic labeling on a graph with v vertices and e edges will be defined as a one-to-one map taking the vertices and edges onto the integers 1, 2, ... , v+e with the property that the sum of the label on an edge and the labels of its endpoints is constant independent of the choice of edge. Prope...

In this paper, a generalization of a group-magic graph is introduced and studied. Let R be a commutative ring with unity 1. A graph G = (V,E) is called R-ring-magic if there exists a labeling f : E → R−{0} such that the induced vertex labelings f : V → R, defined by f(v) = Σf(u, v) where (u, v) ∈ E, and f : V → R, defined by f(v) = Πf(u, v) where (u, v) ∈ E, are constant maps. General algebraic...