Related papers: A construction of magic 24-cells
Magic squares are a fascinating mathematical challenge that has intrigued mathematicians for centuries. Given a positive (and possibly large) integer \( n \), one of the main challenges that still remains is to find, within a computational…
We consider the notion of a signed magic array, which is an $m \times n$ rectangular array with the same number of filled cells $s$ in each row and the same number of filled cells $t$ in each column, filled with a certain set of numbers…
In general graph theory, the only relationship between vertices are expressed via the edges. When the vertices are embedded in an Euclidean space, the geometric relationships between vertices and edges can be interesting objects of study.…
The Antimagic Graph Conjecture asserts that every connected graph $G = (V, E)$ except $K_2$ admits an edge labeling such that each label $1, 2, \dots, |E|$ is used exactly once and the sums of the labels on all edges incident to a given…
We describe how to construct and enumerate Magic squares, Franklin squares, Magic cubes, and Magic graphs as lattice points inside polyhedral cones using techniques from Algebraic Combinatorics. The main tools of our methods are the Hilbert…
This paper aims to address the relation between a magic square of odd order $n$ and a group, and their properties. By the modulo number $n$, we construct entries for each table from initial table of magic square with large number $n^2$.…
We analyze polyhedra composed of hexagons and triangles with three faces around each vertex, and their 3-regular planar graphs of edges and vertices, which we call "trihexes". Trihexes are analogous to fullerenes, which are 3-regular planar…
In this short paper we have produced different kinds of upside down magic squares based on a palindromic day 11.02.2011. In this day appear only the algorisms 0, 1 and 2. Some of the magic squares are bimagic and some are palindromic. Magic…
The new International System of Units may let us select an integer value for Avogadro's number. Some might prefer an integer that's divisible by 12, so that an integer number of $^{12}C$ atoms may be associated (to first order) with a…
The enumeration of chemical graphs is an important topic in cheminformatics and bioinformatics, particularly in the discovery of novel drugs. These graphs are typically either tree-like multigraphs or composed of tree-like multigraphs…
Flip-graph connectedness is established here for the vertex set of the 4-dimensional cube. It is found as a consequence that this vertex set has 92 487 256 triangulations, partitioned into 247 451 symmetry classes.
Fullerenes are an allotrope of carbon having hollow, cage-like structure. Atoms in the molecule are arranged in pentagonal and hexagonal rings, such that each atom is connected to three other atoms. Simple polyhedra having only pentagonal…
We systematically investigate properties of various triangle centers (such as orthocenter or incenter) located on the four faces of a tetrahedron. For each of six types of tetrahedra, we examine over 100 centers located on the four faces of…
The super edge-magicness of graphs of equal order and size has been shown to be important since such graphs can be used as seeds to answer many questions related to (super) edge-magic labelings and other types of well studied labelings, as…
The request for high-quality solutions continually grows in a world where more and more tasks are executed through computers. This also counts for fields such as engineering, computer graphics, etc., which use meshes to solve their…
For a graph on $m$ edges, a bijective function between the edge set of the graph and $\{1,2,\ldots,m\}$ is an antimagic labeling provided that when adding the labels of the edges incident to the same vertex, the sums are pairwise distinct.…
The edge-to-edge tilings of the sphere by congruent quadrilaterals of Type $a^2bc$ are classified as $3$ classes: a sequence of two-parameter families of $2$-layer earth map tilings with $2n$ $(n\ge3)$ tiles, a one-parameter family of…
We report recent progress in the problem of distinguishing convex subsets of cyclotomic model sets $\varLambda$ by (discrete parallel) X-rays in prescribed $\varLambda$-directions. It turns out that for any of these model sets $\varLambda$…
In this paper, we study the concept of "binary color-coded magic squares" by assigning two distinct colors to the even and odd numbers within a magic square. We investigate the uniqueness of patterns within these squares using three…
We introduce a variant of the vertex-distinguishing edge coloring problem, where each edge is assigned a subset of colors. The label of a vertex is the union of the sets of colors on edges incident to it. In this paper we investigate the…