Vertex-Magic Graphs

In graph theory, a graph labeling is an assignment of labels to the edges and vertices of a graph. There are many different types of graphs labelings. Some include graceful labelings, harmonious labelings, and magic labelings. In this project we will focus on a type of magic labeling. A vertex-magic total labeling is a labeling such that the vertices and edges are assigned consecutive integers between 1 and v+e, where v is the order of the graph and e is the size of the graph. When the sum of the labels of a vertex and its incident edges results in the same integer for each vertex, we have a vertex-magic total labeling. This integer is called the magic number of the graph and the graph is called a vertex-magic graph. There has been previous research on vertex-magic total labelings and we know a lot about certain classes of graphs. In this project, we are considering crown graphs. We will give upper and lower bounds of the magic number, a function that generates vertex-magic total labelings of crown graphs and discuss other results about this kind of labeling

E-super vertex magic labelling of graphs and some open problems

Let G be a finite graph with p vertices and q edges. A vertex magic total labelling is a bijection from the union of the vertex set and the edge set to the consecutive integers 1, 2, 3, . . . , p + q with the property that for every u in the vertex set, the sum of the label of u and the label of the edges incident with u is equal to k for some constant k. Such a labelling is E-super, if the labels of the edge set is the set {1, 2, 3, . . . , q }. A graph G is called E-super vertex magic, if it admits an E-super vertex magic labelling. In this paper, we establish an E-super vertex magic labelling of some classes of graphs and provide some open problems related to it

On Consecutive labeling of plane graphs

This paper concerns a labeling problem of the plane graphs Pmn. The present paper describes a magic vertex labeling and a consecutive labeling of type (0,1,1). These labelings combine to a consecutive labeling of type (1,1,1). © 1991

Perfect (super) Edge-Magic Crowns

A graph G is called edge-magic if there is a bijective function f from the set of vertices and edges to the set {1,2,…,|V(G)|+|E(G)|} such that the sum f(x)+f(xy)+f(y) for any xy in E(G) is constant. Such a function is called an edge-magic labelling of G and the constant is called the valence. An edge-magic labelling with the extra property that f(V(G))={1,2,…,|V(G)|} is called super edge-magic. A graph is called perfect (super) edge-magic if all theoretical (super) edge-magic valences are possible. In this paper we continue the study of the valences for (super) edge-magic labelings of crowns Cm¿K¯¯¯¯¯n and we prove that the crowns are perfect (super) edge-magic when m=pq where p and q are different odd primes. We also provide a lower bound for the number of different valences of Cm¿K¯¯¯¯¯n, in terms of the prime factors of m.Postprint (updated version

Properties of consecutive edge magic total graphs

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