Magic covering and edge magic labelling and its application Magic covering and edge magic labelling and its application (original) (raw)
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Magic covering and edge magic labelling and its application
Journal of Physics, Conference Series, 2020
Graph theory is developing very rapidly, especially in labelling graphs. This is proven by the number of researches examining graph labelling. In graphs labelling, research focuses on developing theories. On the other hand, graph labelling (magic covering and edge super magic labelling) has a useful application. This paper will discuss the magic covering of a simple graph (Domino graph) and edge magic labelling on a simple graph (Domino graph). The conclusion is that the magic covering can be applied to a secret sharing scheme, and also edge magic labelling can be applied to ruler models.
On 0-Edge Magic Labeling of Some Graphs Research
2017
A graph G = (V,E) where V = {vi, 1 ≤ i ≤ n} and E = {vivi+1, 1 ≤ i ≤ n} is 0-edge magic if there exists a bijection f : V (G)→ {1,−1} then the induced edge labeling f : E → {0}, such that for all uv ∈ E(G), f∗(uv) = f(u) + f(v) = 0. A graph G is called 0-edge magic if there exists a 0-edge magic labeling of G. In this paper, we determine the 0-edge magic labeling of the cartesian graphs Pm × Pn and Cm × Cn, and the generalized Petersen graph P (m,n). MSC: 05C78.
On New Properties of Graphs with Magic Type Labeling
Control Systems and Computers, 2019
We have shown the connection between vertex labelings of magic graph and its overgraph. Also, we have introduced binary relation on the set of all D i-distance magic graphs, where D i ⊂ {0, 1, ..., d}, i = 1, 2, ... and proved, that it is equivalence relation. Therefore, we have explored the properties of the graphs, which are in this relation. Finally, we have offered the algorithm of constructing r-regular handicap graph G = (V, E) of order n, where n ≡ 0(mod8), r ≡ 1,3(mod4) and 3 ≤ r ≤ n-5.
Journal of Algorithms and Computation, 2018
For any non-trivial abelian group A under addition a graph G is said to be A-magic if there exists a labeling f : E(G) → A − {0} such that, the vertex labeling f + defined as f + (v) = f (uv) taken over all edges uv incident at v is a constant. An A-magic graph G is said to be Z k-magic graph if the group A is Z k the group of integers modulo k. These Z k-magic graphs are referred to as k-magic graphs. In this paper we prove that the total graph, flower graph, generalized prism graph, closed helm graph, lotus inside a circle graph, G ⊙ K m , m-splitting graph of a path and m-shadow graph of a path are Z k-magic graphs.
A Heuristic for Magic and Antimagic Graph Labellings
2013
Graph labellings have been a very fruitful area of research in the last four decades. However, despite the staggering number of papers published in the field (over 1000), few general results are available, and most papers deal with particular classes of graphs and methods. Here we approach the problem from the computational viewpoint, and in a quite general way. We present the existence problem of a particular labelling as a combinatorial optimization problem, then we discuss the possible strategies to solve it, and finally we present a heuristic for finding different classes of labellings, like vertex-, edge-, or face-magic, and (a,d)(a, d)(a,d)-antimagic (v,e,f)(v, e, f)(v,e,f)-labellings. The algorithm has been implemented in C++ and MATLAB, and with its aid we have been able to derive new results for some classes of graphs, in particular, vertex-antimagic edge labellings for small graphs of the type P2rtimesP3sP_2^r \times P_3^sP2rtimesP3s, for which no general construction is known so far.
A generalization of magic labeling of two classes of graphs
Bull. ICA, 2019
A k-magic labeling of a finite, simple graph with |V (G)| = p and |E(G)| = q, is a bijection from the set of edges into the set of integers {1, 2, 3, • • • , q} such that the vertex set V can be partitioned into k sets V 1 , V 2 , V 3 , • • • , V k , 1 ≤ k ≤ p, and each vertex in the set V i has the same vertex sum and any two vertices in different sets have different vertex sum, where a vertex sum is the sum of the labels of all edges incident with that vertex. A graph is called k-magic if it has a k-magic labeling. The study of k-magic labeling is very interesting, since all magic graphs are 1-magic and all antimagic graphs are p-magic. The Splendour Spectrum of a graph G, denoted by SSP (G), is defined by SSP (G) = {k | G has a k-magic labeling}. In this paper, we determine SSP (K m,n), m and n are even and SSP (T n), where T n is the friendship graph and n ≥ 1.
2001
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. Properties of these labelings are surveyed and the question of which families of graphs have magic labelings are addressed. 1 Graph labelings All graphs in this paper are finite, simple and undirected (although the imposition of directions will cause no complications). The graph G has vertex-set V(G) and edge-set E(G). A general reference for graph-theoretic ideas is [19].
On Complementary Edge Magic Labeling ofCertain Graphs
American Journal of Mathematics and Statistics, 2012
By G(p, q) we denote a graph having p vertices and q edges, by V(G) and E(G) the vertex set and the edgeset of G respectively. But the vertices and edges are called the elements of the graph. A (p, q)-graph G is called the edgemagic if there exists a bijective function f: V(G) U E(G) {1,2, ,p+q} such that f(u)+f(v)+f(uv)=k is a constant called the valence of f for any edge uv of G. Given an edge magic f of a graph G(p, q) the function () f x such that () f x =p+q+1-f(x) for all elements of G is said to be complementary to f(x) or complementary edge magic labeling () f x. The purpose of this article is to search for certain graphs Km, n (m, n ≥ 1), Cn (n ≥ 3), np2, f n (fan) Bn (bwk) and nG (n ≥ 2) where G is bipartite or tripartite which have complementary edge magic strength.
International Journal of Mathematics And its Applications E k-Super Vertex Magic Labeling of Graphs
2018
Let G be a graph with p vertices and q edges. An Ek-super vertex magic labeling (Ek-SVML) is a bijection f : V (G) ∪ E(G) → {1, 2, . . . , p + q} with the property that f(E(G)) = {1, 2, . . . , q} and for each v ∈ V (G), f(v) + wk(v) = M for some positive integer M . For an integer k ≥ 1 and for v ∈ V (G), let wk(v) = ∑ e∈Ek(v) f(e), where Ek(v) is the set of all edges which are at distance at most k from v. The graph G is said to be Ek-regular with regularity r if and only if |Ek(e)| = r for some integer r ≥ 1 and for all e ∈ E(G). A graph that admits an Ek-SVML is called Ek-super vertex magic (Ek-SVM). This paper contain several properties of Ek-SVML in graphs. A necessary and sufficient condition for the existence of Ek-SVML in graphs has been obtained. Also, the magic constant for Ek-regular graphs has been obtained. Further, we establish E2-SVML of some classes of graphs such as cycles, complement of cycles, prism graphs and a family of circulant graphs. MSC: 05C78.
A heuristic for magic and antimagic graph labelling
VII Spanish Congress on Metaheuristics, and Evolutive and Bioinspired Algorithms, 2010
Edición: 1ª Impresión: 1ª Nº de páginas: 792 Formato: 17 x 24 Materia CDU: 004 Ciencia y tecnología de los ordenadores. Informática