Welcome to MagicStarGraphs
This application is designed to simulate and generate Star-Magic Graphs, particularly Star Graphs that satisfy the Star-Magic Labeling property.
A graph is an ordered pair (V, E), consisting of a vertex set V and an edge set E. It is a mathematical structure used to represent pairwise relations between objects. A vertex and an edge in a graph can be depicted as a point and a line connecting two distinct points, respectively. A subgraph of a graph G is a graph H whose vertex and edge sets are subsets of G.
Let G be a graph. A Star-Magic Labeling of G is a mapping process of assigning positive numbers (from 1 to the number of vertices and edges) to each vertex and edge of G. This assignment must ensure that each subgraph of G, isomorphic to a Star, has the same star-weight sum. In this context, the star-weight sum is the sum of the labels of the vertices and edges associated with the vertices and edges in the subgraph. We call G as a Star-Magic Graph if there exists a mapping that satisfies these properties. The problem is to determine the existence of a Star-Magic Labeling for a given graph G. In this case, we consider G as Star Graph, denoted by Sn, for integer n>3.
Aside from the theoretical aspect, we can consider a Star-Magic Labeling as a type of Mathematical Puzzle involving a star-shaped arrangement of numbers. The goal is to place numbers (from 1 to the number of vertices and edges) on each of the Star’s vertices and edges so that each subgraph, isomorphic to a star, has an equal star-weight sum.
Star-Magic Graphs can be visualized using a graph, where each vertex represents a point in the star, and each edge represents the connections between two points, forming a geometric shape that aids in solving and understanding the numerical relationships within the puzzle.