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Some results concerning the valences of (super) edge-magic graphs
A graph is called edge-magic if there exists a bijective function
such that is a constant (called the valence of ) for each . If , then is called a super
edge-magic graph. A stronger version of edge-magic and super edge-magic graphs
appeared when the concepts of perfect edge-magic and perfect super edge-magic
graphs were introduced. The super edge-magic deficiency of a graph is defined to be either the smallest
nonnegative integer with the property that is super
edge-magic or if there exists no such integer . On the other
hand, the edge-magic deficiency of a graph is the
smallest nonnegative integer for which is edge-magic, being
always finite. In this paper, the concepts of (super)
edge-magic deficiency are generalized using the concepts of perfect (super)
edge-magic graphs. This naturally leads to the study of the valences of
edge-magic and super edge-magic labelings. We present some general results in
this direction and study the perfect (super) edge-magic deficiency of the star
Recent studies on the super edge-magic deficiency of graphs
A graph is called edge-magic if there exists a bijective function
such that is a constant for each . Also,
is said to be super edge-magic if . Furthermore, the
super edge-magic deficiency of a graph is defined
to be either the smallest nonnegative integer with the property that is super edge-magic or if there exists no such integer
. In this paper, we introduce the parameter as the minimum
size of a graph of order for which all graphs of order and size at
least have , and provide
lower and upper bounds for . Imran, Baig, and
Fe\u{n}ov\u{c}\'{i}kov\'{a} established that for integers with , , where is the
cartesian product of the cycle of order and the complete graph
of order . We improve this bound by showing that when is even. Enomoto,
Llad\'{o}, Nakamigawa, and Ringel posed the conjecture that every nontrivial
tree is super edge-magic. We propose a new approach to attak this conjecture.
This approach may also help to resolve another labeling conjecture on trees by
Graham and Sloane
New Results on the (Super) Edge-Magic Deficiency of Chain Graphs
Let G be a graph of order v and size e. An edge-magic labeling of G is a bijection f:V(G)∪E(G)→{1,2,3,…,v+e} such that f(x)+f(xy)+f(y) is a constant for every edge xy∈E(G). An edge-magic labeling f of G with f(V(G))={1,2,3,…,v} is called a super edge-magic labeling. Furthermore, the edge-magic deficiency of a graph G, μ(G), is defined as the smallest nonnegative integer n such that G∪nK1 has an edge-magic labeling. Similarly, the super edge-magic deficiency of a graph G, μs(G), is either the smallest nonnegative integer n such that G∪nK1 has a super edge-magic labeling or +∞ if there exists no such integer n. In this paper, we investigate the (super) edge-magic deficiency of chain graphs. Referring to these, we propose some open problems
Super edge-magic deficiency of join-product graphs
A graph is called \textit{super edge-magic} if there exists a bijective
function from to such
that and is a
constant for every edge of . Furthermore, the \textit{super
edge-magic deficiency} of a graph is either the minimum nonnegative integer
such that is super edge-magic or if there exists no
such integer.
\emph{Join product} of two graphs is their graph union with additional edges
that connect all vertices of the first graph to each vertex of the second
graph. In this paper, we study the super edge-magic deficiencies of a wheel
minus an edge and join products of a path, a star, and a cycle, respectively,
with isolated vertices.Comment: 11 page
Super Edge-magic Labeling of Graphs: Deficiency and Maximality
A graph G of order p and size q is called super edge-magic if there exists a bijective function f from V(G) U E(G) to {1, 2, 3, ..., p+q} such that f(x) + f(xy) + f(y) is a constant for every edge and f(V(G)) = {1, 2, 3, ..., p}. The super edge-magic deficiency of a graph G is either the smallest nonnegative integer n such that G U nK_1 is super edge-magic or +~ if there exists no such integer n. In this paper, we study the super edge-magic deficiency of join product graphs. We found a lower bound of the super edge-magic deficiency of join product of any connected graph with isolated vertices and a better upper bound of the super edge-magic deficiency of join product of super edge-magic graphs with isolated vertices. Also, we provide constructions of some maximal graphs, ie. super edge-magic graphs with maximal number of edges
Problemas abiertos sobre etiquetamientos super edge-magic y temas relacionados
El tema de los etiquetamientos de grafos ha experimentado un fuerte impulso
en los últimos 40 años, muestra de ello son los dos libros dedicados en exclusiva
a ellos, un completísimo artículo ”survey” y más de 1000 artículos en la literatura.
En este artículo exploramos algunas preguntas abiertas sobre etiquetamientos super
edge-magic. Nos interesa particularmente este tipo de etiquetamientos, debido a
la cantidad de relaciones que poseen con otras clases de etiquetamientos, principalmente
los graciosos y los armónicos.Preprin
Magic and antimagic labeling of graphs
"A bijection mapping that assigns natural numbers to vertices and/or edges of a graph is called a labeling. In this thesis, we consider graph labelings that have weights associated with each edge and/or vertex. If all the vertex weights (respectively, edge weights) have the same value then the labeling is called magic. If the weight is different for every vertex (respectively, every edge) then we called the labeling antimagic. In this thesis we introduce some variations of magic and antimagic labelings and discuss their properties and provide corresponding labeling schemes. There are two main parts in this thesis. One main part is on vertex labeling and the other main part is on edge labeling."Doctor of Philosoph
PENGEMBANGAN BAHAN AJAR MATA KULIAH STUKTUR DATA BERBASIS WEB
Internet merupakan sebuah revolusi dalam perkembangan teknologi digital yang
ditandai dengan terjadinya konvergensi antara teknologi komunikasi, komputer, dan
penyiaran (broadcasting) menjadi sebuah teknologi informasi. Internet menjadi jaringan
informasi dan komunikasi global pada masa kini
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