For example, consider, the following graph G The graph G has deg(u) = 2, deg(v) = 3, deg(w) = 4 and deg(z) = 1. Regular Graph A graph is regular if all the vertices of G have the same degree. In particular, if the degree of each vertex is r, the G is regular of ...
For example, in graceful labeling, the difference between the labels of two connected vertices is equal to the label of the edge joining them. Injective or Surjective Mappings: The labels may be required to form injective (unique mapping) or surjective (covering a range) mappings. Modulo ...
Graph theory is also widely used in sociology as a way, for example, to measure actors' prestige or to explore rumor spreading, notably through the use of social network analysis software. Under the umbrella of social networks are many different types of graphs. Acquaintanceship and friendship gr...
Graph Theory Examples - Explore various examples of graph theory concepts, including practical applications and problem-solving techniques in this tutorial.
Learn about graph theory and how trees are used to solve complex problems. Discover the beauty and simplicity of tree structures. Start exploring now!
A graph is a complete graph if any two vertices in the graph are adjacent.Definition: Closed and CycleClosedIf the initial vertex and the final vertex is the same in a walk, this walk is closed.CycleIf a path is closed, it is a cycle....
Some Examples from Graph Theory As the title suggests, this chapter will introduce some examples where the Catalan numbers arise in graph theory. In Chapter 12, we were introduced to the structure called an undirected graph. In our first example, we shall investigate a special collection of undi...
We have an innate preference for structural symmetry and rational layering. In graph theory, this is known asstructural balance. A structurally balanced triadic closure is made of relationships of all strong, positive sentiments (such as the first example below) or of two relationships with negative...
Graph Products in Graph Theory - Explore the various graph products in graph theory, including Cartesian product, tensor product, and more. Understand their properties and applications.
Graph theory is a branch of combinatorics that specializes in modeling relationships between objects. For instance, the objects may be individuals and they are related if they are acquainted. As a second example, suppose that our objects are airports. We would say that two airports are related ...