Some results concerning the valences of (super) edge-magic graphs

A graph $G$ is called edge-magic if there exists a bijective function $f:V\left(G\right) \cup E\left(G\right)\rightarrow \left\{1, 2, \ldots , \left\vert V\left( G\right) \right\vert +\left\vert E\left( G\right) \right\vert \right\}$ such that $f\left(u\right) + f\left(v\right) + f\left(uv\right)$ is a constant (called the valence of $f$) for each $uv\in E\left( G\right)$. If $f\left(V \left(G\right)\right) =\left\{1, 2, \ldots , \left\vert V\left( G\right) \right\vert \right\}$, then $G$ 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 $\mu_{s}\left(G\right)$ of a graph $G$ is defined to be either the smallest nonnegative integer $n$ with the property that $G \cup nK_{1}$ is super edge-magic or $+ \infty$ if there exists no such integer $n$. On the other hand, the edge-magic deficiency $\mu\left(G\right)$ of a graph $G$ is the smallest nonnegative integer $n$ for which $G\cup nK_{1}$ is edge-magic, being $\mu\left(G\right)$ 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 $K_{1,n}$

Super edge-magic deficiency of join-product graphs

A graph $G$ is called \textit{super edge-magic} if there exists a bijective function $f$ from $V(G) \cup E(G)$ to $\{1, 2, \ldots, |V(G) \cup E(G)|\}$ such that $f(V(G)) = \{1, 2, \ldots, |V(G)|\}$ and $f(x) + f(xy) + f(y)$ is a constant $k$ for every edge $xy$ of $G$. Furthermore, the \textit{super edge-magic deficiency} of a graph $G$ is either the minimum nonnegative integer $n$ such that $G \cup nK_1$ is super edge-magic or $+\infty$ 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 $xy \in E(G)$ 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

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

IMPLEMENTASI JARINGAN SARAF TIRUAN (JST) DALAM PREDIKSI KEBANGKRUTAN

Prediksi kebangktutan (bankruptcy prediction) merupakan masalah klasifikasi. Ketersediaan data financial dan akunting yang menjadi variable input memungkinkan digunakannya jaringan saraf tiruan (JST) dalam kebangrutan sebuah perusahaan. Tulisan ini membahas implementasi JST dalam prediksi kebangkrutan dan membandingkan penggunaannya untuk single layer network dan multiple layer network

INDIKASI BAHWA OBJEK-OBJEK MATEMATIKA DAPAT DIPANDANG SEBAGAI BARISAN STRUKTUR-STRUKTUR HINGGA

Makalah ini memaparkan semacam ultraproduk dari teori himpunan hingga di mana ultrafilternya merupakan filter Frechet yaitu subhimpunan-subhimpunan kofinit (komplemennya hingga) dari himpunan semua bilangan asli

Montana Kaimin, November 8, 1991

Student newspaper of the University of Montana, Missoula.https://scholarworks.umt.edu/studentnewspaper/9460/thumbnail.jp

INDIKASIBAHWA OBJEK-OBJEK MATEMATIKA DAPAT DIPANDANG SEBAGAI BARISAN STRUKTUR-STRUKTUR HINGGA

Makalah ini memaparkan semacam ultraproduk dari teori himpunan hingga di mana ultrafilternya merupakan filter Frechet yaitu subhimpunan-subhimpunan kofinit (komplemennya hingga) dari himpunan semua bilangan asli. Pengkhususan ini dimaksudkan untuk membuat aksiomatisai menjadi lebih mudah dalam rangka melihat bahwa pada dasarnya teori himpunan biasa tertanam di dalam perumusan baru ini, sedangkan yang terakhir ini menampilkan objek-objeknya selalu sebagai barisan\ud (berdomain bilangan asli) dari himpunan-himpunan hingga. Sepintas lalu mungkin terlihat kontradiktif menyatakan himpunan dengan sembarang kardinalitas dengan barisan himpunan hingga namun teori himpunan yang dibicarakan adalah di dalam bahasa "ultraproduk" dan bukan dalam bahasa yang sarna dengan bahasa "barisan objekobjek hingga". Ini menjelaskan kesan paradoksal tadi