Graph labeling is one of the fascinating areas of graph theory with wide ranging applications. The constant h is called the magic constant for again, a graph with a vertexmagic total labeling will be called vertexmagic. The star graphs has vertex bimagic total labeling for all, but does not have vertex magic total labeling for proof. A magic graph is a graph whose edges are labelled by positive integers, so that the sum over the edges incident with any vertex is the same, independent of the choice of vertex. An vertexantimagic edge labeling or an vae labeling, for short of is. A total labeling f is said to be a vertexmagic total labeling vmt labeling if the weight of each vertex is equal to the same constant k, called the magic constant of the vmt labeling. In theorem 3, we found a way to construct vatl for a. A graph is called super edgemagic total semt if it admits a super edgemagic total labeling. General result on the even vertex magic total labeling of t copies of isomorphic suns, for any integers t 1 is given. The main method of construction is to assemble a number of appropriately labeled copies of one graph into a single graph with a vmtl. Labeling schemes are given for connected and disconnected graphs in addition to wellknown graph families. Even vertex magic total labeling of isomorphic and non.
Apart from duality, how can a vertexantimagic total labeling for a graph be used to construct another vertexantimagic total labeling for the same graph, preferably with different a and d. Algorithms to realize all possible vertex magic total labeling and. The notion of a vsuper vertex magic labeling was introduced by macdougall et al. If all the vertices in g have the same weight k, we call the labeling vertexmagic labeling or vertexmagic total. In 14, froncek, kovar, and kovarova proved the following about vertex magic total labelings of a product of cycles. A graph is called perfect super edgemagic if all theoretical super edgemagic valences are possible. Professor miller launched the successful conference series iwogl international workshop on graph labelings. Super edge antimagic total labeling of fully generalized. Algorithms to realize all possible vertex magic total. Vertexantimagic total labelings of graphs discussiones. Nalliah, super a,dedge antimagic total labeling of friendship and generalized friendship graphs, electronic notes in discrete mathematics, 48 2015, 103110. A labeling of graph g is a mapping that carries a set of graph elements into a set of numbers usually positive integers called labels.
One type of graph that has interesting vertexmagic properties is the cycle graph. L21 graph processing free download as powerpoint presentation. Cn has a super vertexmagic total labeling if and only if n is odd. Esuper vertex magic labelling of graphs and some open. Dr joe ryan staff profile the university of newcastle. Rfid and barcode labeling software solutions cybra. Vertexmagic labelings of regular graphs ii sciencedirect. Pdf algorithm to construct super vertex magic total labeling of. Buy studies in graph theory magic labeling and related concepts book online at best prices in india on. Vertexmagic graphs are graphs labeled with numbers in which every vertex and its incident edges add up to the same number. Graph cn admits vsuper vertex magic labeling and esuper vertex magic labeling only if n. However, with the aid of computer programs, we have found that admits an vae labeling for.
I found this problem in pearls in graph theory by hartfield and ringel in the chapter labeling graphs. This means that, in order to see whether a given graph is magic, it suffices to. Vertex magic group edge labelings swenson college of. Under a total labeling, vertexweight of v is defined as the sum of the label of v and the edge labels corresponding to the entire edges incident with v. Powerful and easy to use, once you try markmagic, youll see why thousands of software vendors and customers worldwide rely on the software to create. A dynamic survey of graph labeling electronic journal of. Specifically, this is an exposition of the results of the paper vertexantimagic total labelings of graphs by m. On the degrees of a strongly vertexmagic graph sciencedirect. It is easy to see that if a is a magic labeling with magic sum k then x is a magic labeling with magic sum k 3m k.
On complementary edge magic labeling ofcertain graphs. We also found kinda long article about converting vtml to sat article. E super vertex magic labeling the magic constant is denoted by k m. In this paper we present a new algorithm to obtain any desired magic constant within the allowable range using the concepts of subset construction and magic square. Pdf on mar 1, 20, krishnappa h k and others published algorithms to realize all possible vertex magic total labeling and super vertex. Markmagic barcode labeling software is the easiest way to design and print the barcode labels, electronic forms, reports, and rfid tags you need to communicate with your customers and suppliers.
Howev er, we will also provide the valences to increase. In addition, it is called super a, dedge antimagic total labeling if vertices receive the smallest. Kotzig and rosa 10 define a magic labeling to be a total labeling in which the. Strong super edge magic labelings are introduced and relationships between super edge magic total labelings and other labeling schema are explored. Sugeng entitled magic and antimagic labeling of graphs. An enormous body of literature has grown around graph labeling in the last five decades. The super vertex magic total labeling of a graph is the vertex magic labeling with the condition that all the vertices of the takes the labels 1,2,3. After vertex magic total labelings, this chapter has a focus on edge magic total labelings. The information of a packet is applied with labeling and if it is satisfying magic labeling on a particular magic constant k, than packet consist 1, k, one of the label for each vertex i.
We need to find a magic labeling of the octahedron graph. She was part of various teams that introduced such graph labeling schemes as vertex antimagic total labeling vatl, edge antimagic total labeling eatl, edge irregular total labeling and vertex irregular total labeling. The star graph be with vertices and edges with the bijection as with, we find that the values when but when. Markmagic barcode label printing software cybra corporation. A graph labeling is an assignment of integers to the vertices or edges, or both, subject to. Pdf on jan 1, 20, krishnappa h k and others published algorithm to construct super vertex magic total labeling of complete graphs.
Me and my friends receive the problem from title to resolve. A dynamic survey of graph labeling the electronic journal of. If each vertex has the same weight, then the total labeling. Vertexmagic total labelings were introduced in 14 and a good. They call a vertex magic total labelling is super, if feg 1, 2. The class of totally magic graphs those which admit a totally magic labeling is much more restricted than the edgemagic or vertexmagic graphs. Studies in graph theory magic labeling and related. We establish the existence of vertexmagic total labelings vmtls for several infinite classes of regular graphs. A vertex magic total labeling is a bijection f from vg eg to the integers 1. We also show that some graphs admits e super vertex magic labeling and v super vertex magic labeling simentiously but some not 1, 2, 3, 6. If the integers are the first q positive integers, where q is the number of edges, the graph and the labelling are called supermagic. Figure 2 gives an example of a totally magic labeling on the cycle c3. By gp, q we denote a graph having p vertices and q edges, by vg and eg the vertex set and the edge set of g respectively. A p, q graph g is called the edge magic if there exists a bijective function f.
Before looking at e super vertex magic labeling and v super vertex magic labeling, we first look at some basic concepts and definitions of graph theory. On vertexantimagic edge labeling of regular graphs hindawi. Graph labelings were first introduced in the 1960s where the vertices and edges are assigned real values or subsets of a set subject to certain conditions. This is a graph with 4 vertices and 3 edges as given below. Jeyanthi 2003 introduced a concept with the name super vertex magic labelling, but with different notion. Super edgemagic total labeling adalah edgemagic total labeling dimana label dari vertex adalah 1, 2, dan. We found nice and easy to use sat solver cryptominisat. Magic and antimagic graphs attributes, observations and. Marimuthu, esuper vertex inmagic total labeling of digraphs, electronic notes in discrete mathematics, 48 2015, 111118. The following proposition presents the relation between a. Magic labelings on cycles and wheels university of guelph. A vmtl is super if all the smallest labels are assigned to the vertices. In this paper we construct new families of trees using wtrees 15 referred as reflexive wtrees and prove that they are super edge magic total. Ijamss v super and e super vertex magic total labeling.
Buy studies in graph theory magic labeling and related. Edgemagic total labelings the australasian journal of. The constants k 1 and k 2 are called magic constants. Enomoto et al 4 have introduced the name super edgemagic for magic labelings in. Computing edgeweight bounds of antimagic labeling on a class. Super vertex magic and esuper vertex magic total labelling.
Applications of graph labeling in communication networks. It is still unknown what types of graphs are vertexmagic and which are not. An interesting open problem is whether it is possible to find a super edgemagic labeling for a general merge graph tm sn for m 2, n 1. A graph with vertex magic total labeling with two constants k 1 or k 2 is called a vertex bimagic total labeling and denoted by vbmtl.
A supermagic labeling of a graph is an edge weighting where the edge weights are consecutive integers thats the super part, and where if you label each vertex with the sum of the weights of its incident edges, you get the same label on each vertex. Vertexmagic labeling of regular graphs acm digital library. To avoid confusion, marimuthu and balakrishnan 2012 called a total labelling as an esuper vertex magic total labelling, if fe 1, 2. A super edge magic total labeling is an edge magic total labeling f which fv 1, v. L21 graph processing map reduce vertex graph theory. Super edgemagic total labeling dari subdivision star,, di mana 5, 3 dan 1 merupakan masalah yang belum terpecahkan. A vmt labeling is said to be a super vmt labeling if the vertices are labeled with the smallest possible integers, 1, 2, v. But the vertices and edges are called the elements of the graph. It is a classical problem to construct new classes of super edge magic total graphs using old ones.
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