Our purpose is to introduce a linear-algebraic construction for magic rectangles of size pr × ps, where p is prime and 1 ≤ r ≤ s. For fixed p, r, and s, this method allows for the production of many different magic rectangles. It follows that, for many non-coprime dimensions, this construction will significantly augment the sparse collection of “known” magic rectangles. A magic rectangle of siz...

let $a$ be a non-trivial abelian group and $a^{*}=asetminus {0}$. a graph $g$ is said to be $a$-magic graph if there exists a labeling$l:e(g)rightarrow a^{*}$ such that the induced vertex labeling$l^{+}:v(g)rightarrow a$, define by $$l^+(v)=sum_{uvin e(g)} l(uv)$$ is a constant map.the set of all constant integerssuch that $sum_{uin n(v)} l(uv)=c$, for each $vin n(v)$,where $n(v)$ denotes the s...

In this paper, we consider special class of trees called uniform k-distant trees, which have many interesting properties. We show that they have an edge-magic total labeling, a super edge-magic total labeling, a (a, d)-edge-antimagic vertex labeling, an (a, d)-edgeantimagic total labeling, a super (a, d)edge-antimagic total labeling. Also we introduce a new labeling called edge bi-magic vertex ...

A graph G is called super edge-magic if there exists a bijective function f : V (G) ∪ E (G) → {1, 2, . . . , |V (G)|+ |E (G)|} such that f (V (G)) = {1, 2, . . . , |V (G)|} and f (u) + f (v) + f (uv) is a constant for each uv ∈ E (G). A graph G with isolated vertices is called pseudo super edge-magic if there exists a bijective function f : V (G) → {1, 2, . . . , |V (G)|} such that the set {f (...

Associated to any complex simple Lie algebra is a non-reductive complex Lie algebra which we call the intermediate Lie algebra. We propose that these algebras can be included in both the magic square and the magic triangle to give an additional row and column. The extra row and column in the magic square correspond to the sextonions. This is a six-dimensional subalgebra of the split octonions w...

ABSTRACT Magic labelings of graphs are studied in great detail by Stanley in [18] and [19], and Stewart in [20] and [21]. In this article, we construct and enumerate magic labelings of graphs using Hilbert bases of polyhedral cones and Ehrhart quasi-polynomials of polytopes. We define polytopes of magic labelings of graphs and digraphs. We give a description of the faces of the Birkhoff polytop...

Recent articles calling for a scientific study of magic have been the subject of widespread interest. This article considers the topic from a broader perspective and argues that to engage in a science of magic, in any meaningful sense, is misguided. It argues that those who have called for a scientific theory of magic have failed to explain either how or why such a theory might be constructed, ...

Let G = (V,E) be a graph of order p and size q. It is known that if G is super edge-magic graph then q ≤ 2p− 3. Furthermore, if G is super edge-magic and q = 2p− 3, then the girth of G is 3. It is also known that if the girth of G is at least 4 and G is super edge-magic then q ≤ 2p − 5. In this paper we show that there are infinitely many graphs which are super edge-magic, have girth 5, and q =...

ON SUPER EDGE-MAGIC TOTAL LABELING OF REFLEXIVE W-TREES Muhammad Imran, Mehar Ali Malik, M. Yasir Hayat Malik Department of Mathematics, School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Islamabad, Pakistan. E-mail: {imrandhab, alies.camp, yasirmalikawan}@gmail.com Mathematics Subject Classification: 05C78 ABSTRACT. Kotzig and Rosa [17] defined a magic lab...

We present a new technique for the optimization of (partially) bound queries over disjunctive datalog programs. The technique exploits the propagation of query bindings, and extends the Magic-Set optimization technique (originally defined for non-disjunctive programs) to the disjunctive case, substantially improving on previously defined approaches. Magic-Set-transformed disjunctive programs fr...