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. In this paper, we are studying vertexmagic total labelings vmtls of simple graphs. In this chapter we study edge bimagic labeling, edge antimagic labeling and 1 vertex bimagic vertex labeling. Esuper vertex magic labelling of graphs and some open. Solution to some open problems on esuper vertex magic total.
It is total magic if its edges and vertices can be labelled so that the vertex label plus the sum of labels on edges incident with that vertex is a constant. A graph is vertex magic if its vertices can be labelled so that the sum on any edge is the same. In that labeling, the in that labeling, the edges labelled 1 and 3 which total to 4 are incident with vertex 7 and the edge. A labeling is an assignment of labels to edges, vertices, or both edges and vertices of a graph. Further we investigated the properties of such labeling on these graphs. E with jej k is a bijection ffrom eto an abelian group of order ksuch that the sum of labels of all incident edges of every vertex x2v, called the weight of xand. Uni convert vertex total magic labeling problem to sat. A vertex magic total labeling vmtl of a graph is defined as a onetoone mapping taking the vertices and edges onto the set of integers 1, 2.
In this case, the graph is called an edgelabeled graph. The situation is quite different from the conjectured behavior of edgemagic total labelings of these graphs. Pdf graph labeling vertex antimagic total labeling of. E super vertex magic labeling the magic constant is denoted by k m. Cn has super vertex magic total labeling if and only if n is odd, and no wheel, ladder, fan, friendship graph, complete bipartite graph or graph with a vertex of degree 1 has a super vertex magic total labeling. Hence if n 4 is even and m 1 then the non hamiltonian p m a c n admits modk vertex magic labeling. On antimagic labeling for graph products sciencedirect. Subtractive magic and antimagic total labeling for basic. In this paper, we established some properties of super vertex magic trees and exhibit super vertexmagic labeling of. Pdf on vertexmagic labeling of complete graphs researchgate. Friendship graphs, magic labeling, vertex magic total labeling, edge magic total labeling, total magic labeling are as follows.
A totally magic labeling is a labeling which is simultaneously both a vertex magic total labeling and an edge magic total labeling. An interesting vertex labeling with numbers is vertex magic. It is proved that all cycles have vertex magic total labeling. A vertex is said to be full if all its incident edges are labeled. Esuper vertex magic labelings of graphs sciencedirect. A digraph d is called an esuper vertex in magic total digraph esvimt digraph if d admits an esvimt labeling. Likewise, an edge labelling is a function of e to a set of labels. The star graphs has vertex bimagic total labeling for all, but does not have vertex magic total labeling for proof. Note that if the smallest numbers are assigned to the edges then the magic constant is. We establish the existence of vertex magic total labelings vmtls for several infinite classes of regular graphs. In this paper, we established some properties of super vertex magic trees and exhibit super vertex magic labeling. The magic constants h and k are not necessarily equal.
Macdougall school of mathematical and physical sciences the university of newcastle nsw 2308 australia abstract in this paper, we are studying vertex magic total labelings vmtls of simple graphs. Suppose an odd vertex magic total labeling f of c n exists with the magic constant k. For a bipartite graph with partite sets v 1 and v 2. To avoid confusion, marimuthu and balakrishnan marimuthu and balakrishnan, 2012 called a total labeling f as an esuper vertex magic total labeling if. May 11, 2012 let g v,e be a finite, simple and undirected graph with p vertices and q edges. Uni convert vertextotalmagiclabeling problem to sat. This paper is about the properties of the general graphs like cycle, path, complete, wheel, bipartite and tree which satisfy the vertex magic total labeling. 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. Formally, given a graph g v, e, a vertex labelling is a function of v to a set of labels. A connected graph g is said to admit semi magic labeling, if the edges are labeled with integers such that for each vertex v the sum of the labels of all edges incident with v is same for all v. In this paper we present several properties of esvimt digraphs.
The reverse super vertex magic labeling of a graph is the reverse vertex magic labeling with the condition that all the vertices of the graph takes the labels 1,2,3, v. In this paper, we introduce the concept of fuzzy bi magic labeling in graphs. They called a vertex magic total labelling f to be super if f. The constant h is called the magic constant for again, a graph with a vertexmagic total labeling will be called vertexmagic. This is a graph with 4 vertices and 3 edges as given below. Our main goal is to find a vmtl for each feasible value of h. Cycle is a graph where there is an edge between the adjacent vertices only and the vertex is adjacent to last one fig1. Pdf vertexmagic total labelings of wheels and related.
The astute reader will recognize that taking q 0 gives the upper bound for h in the abstract, while taking q m1 will give the lower bound. A graph with such a function defined is called a vertex labeled graph. A totally magic labeling is a labeling which is simultaneously both a vertexmagic total labeling and an edgemagic total labeling. In general, a magic type labeling is a labeling in which we require the sum of labels related to a vertex for a vertex magic labeling or to an edge for an edge magic labeling to be constant throughout the entire graph. One type of graph that has interesting vertex magic properties is the cycle graph. A vertex magic total labeling is a bijection f from. Vertexmagic labeling of nonregular graphs the australasian. The mirror graph mg of g is obtained from g and g 0 by joining each vertex of v 2 to its corresponding vertex in v 2 0 by an edge. A vertex magic total labeling is an assignment of the integers 1, 2. It is still unknown what types of graphs are vertex magic and which are not. If all the vertices in g have the same weight k, we call the labeling vertex magic labeling or vertex magic total labeling respectively and we call k a magic. Vertexmagic labeling of regular graphs acm digital library. Let sp be the sum of all vertex labels and let sq be the sum of all edge labels. A vertexmagic labeling is an assignment of the integers from 1, 2, 3.
A vertexmagic total labeling vmtl on a graph with v vertices and e edges is a onetoone. Super vertexmagic total labelings of graphs semantic. A vertexmagic labeling f is called super vertexmagic labeling if f e 1, 2, 3. If the vertices are pair wise different then it will be vertex antimagic labeling. We study some of the basic properties of such labelings, find some families of graphs that admit super vertex magic labelings and show that some other families of graphs do not. Vertex magic graphs are graphs labeled with numbers in which every vertex and its incident edges add up to the same number. A graph g is called a super vertex magic if there exists a super vertex magic labeling of g. The constants k 1 and k 2 are called magic constants. For a graph g with v vertices and e edges if there is a one to one function from set of integers 1,2,e to edges of graph and vertices will be assigned label as sum of edges incident to it. For any abelian group a, a graph g v, e is said to be a magic if there exists a labeling l.
A super edge magic labeling of t6s2 figure 6 concluding observations we have obtained results similar to theorem 3. Various authors have introduced labelings that generalize the idea of a magic square. Vertex magic total labeling of generalized petersen graphs. Vertex magic total labeling of completegraphs and their. Bounds on this socalled magic number are found for cycle graphs. An interesting open problem is whether it is possible to find a super edge magic labeling for a general merge graph tm sn for m 2, n 1. Fuzzy bimagic labeling on cycle graph and star graph. The class of totally magic graphs those which admit a totally magic labeling is much more restricted than the edgemagic or vertexmagic graphs. In this paper we prove some existence or nonexistence.
In this section, we prove some basic properties of esuper vertex magic labeling. Universitycollege student higher education 3 days ago uni convert vertex total magic labeling problem to sat. The star graph be with vertices and edges with the bijection as with, we find that the values when but when. An edgegraceful labelling on a simple graph without loops or multiple edges on p vertices and q edges is a labelling of the edges by distinct integers in 1, q such that the labelling on the vertices induced by labelling a vertex with the sum of the incident edges taken modulo p assigns all values from 0 to p. Vertexantimagic labelings of regular graphs springerlink. Graph cn admits vsuper vertex magic labeling and esuper vertex magic labeling only if n is odd positive integer. Let g 0 be the copy of g and v 1 0 and v 2 0 be the copies of v 1 and v 2.
This sum of labels is referred to as the weight of a vertex or an edge depending on the type of labeling. 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. By now much is known about methods for constructing vmtls for regular graphs. A graph is called anti magic if it admits an anti magic labeling.
Under the function f, there exists modk vml for p m a c n. Magic labeling of a graph was introduced by sedlack 9, the concept. There are a great many variations on the concept of magic labelling of a graph. They conjecture that no tree has a super vertex magic total labeling and that k4n has a. If the integers are the first q positive integers, where q is the number of edges, the graph and the labelling are called supermagic.
An a, d vertex antimagic total labeling of g is a bijection f from v g. Y ponnappan and others published odd vertex magic labeling find, read and cite all the research you need on. By now much is known about methods for constructing. Kotzig and rosa 5, for example, defined a magic labeling to be a labeling. Vertex magic group edge labelings swenson college of.
When the edge labels are members of an ordered set e. We defined fuzzy bi magic labeling for cycle and star graph. Under a total labeling, vertex weight of v is defined as the sum of the label of v and the edge labels corresponding to the entire edges incident with v. However, it will be more convenient to use proposition 3 and instead find the corresponding surjections. A vertex magic labeling of the path p5 is shown in figure 1. Algorithm for vertex antimagic total labeling on various. The main method of construction is to assemble a number of appropriately labeled copies of one graph into a single graph with a vmtl. Distance two vertexmagic graphs ebrahim salehi department of mathematical sciences university of nevada las vegas las vegas, nv 891544020 ebrahim. A graph g is said to be edgegraceful if it admits an. They called a vertex magic total labeling f is super if f. The concept of semi magic labeling was introduced by stewart. An a, dvertexantimagic total labeling of g is a bijection f from v g. Z, in other words it is a labeling of all edges by integers. Solution to some open problems on esuper vertex magic.
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. They called a vertex magic total labelling is super, if fvg 1, 2. E is said to have a distance two magic labeling in a if there exists a labeling l. Then k named a magic constant and g named vertexmagic total graph. They studied the basic properties of vertex magic total graphs and showed some families of graphs having vertex magic total labeling. E with e n is an injection from e to an abelian group. This means that, in order to see whether a given graph is magic, it suffices to. Let g v,e be a finite, simple and undirected graph with p vertices and q edges. It is clearly seen that f is an odd vertex magic total labeling with the magic constant 3 n 2. A graph g is called a super vertexmagic if there exists a super vertexmagic labeling of g. Esuper vertex magic labelling of graphs and some open problems. 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. Raziya begam tree with three vertices and s2 a star on three vertices then t3 s2 is formed as follows.
Magic labelings on cycles and wheels university of guelph. Ijamss v super and e super vertex magic total labeling of. Such a labeling is called an esuper vertex in magic total labeling esvimt labeling if f a 1, 2, 3, q. The constant h is the magic constant for the labeling. Me and my friends receive the problem from title to resolve. Super vertexmagic total labelings of graphs semantic scholar. A detailed survey about magic type labeling is given in the section 1. The class of totally magic graphs those which admit a totally magic labeling is much more restricted than the edge magic or vertex magic graphs. Swaminathan and jeyanthi 2003 introduced a concept with the name super vertex magic labelling, but with different. A vertexmagic total labeling of a graph g is a bijective mapping from v e to 1, 2, 3, h such that for each vertex x in graph g satisfying. Graph labeling vertex anti magic total labeling of sun graph. Pdf vertexmagic total labelings of graphs semantic scholar. A vertex magic total vmt labeling of a graph g v,e is a bijection from the set of vertices and edges to the set of numbers defined by. Then g can be extended to a super vertex magic labeling of g if and only if w u.
The sum of all vertex label and all the edge labels used to calculate the vertex weights is sp. 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. Characterization of connected vertex magic total labeling. Characterization of connected vertex magic total labeling graphs in topological ideals. Cn has super vertex magic total labeling if and only if n is odd. Thus if k is even, p m a c n is a modk vertex magic graph. Let g be a finite graph with p vertices and q edges. A vertex magic labeling f is called super vertex magic labeling if f e 1, 2, 3.
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