What is graph theory for kids?
Graph theory is a field of mathematics about graphs. A graph is an abstract representation of: a number of points that are connected by lines. Each point is usually called a vertex (more than one are called vertices), and the lines are called edges.
What is the first theorem of graph theory?
The following theorem is often referred to as the First Theorem of Graph The- ory. Theorem 1.1. In a graph G, the sum of the degrees of the vertices is equal to twice the number of edges. Consequently, the number of vertices with odd degree is even.
What is a graph problem?
A graph is an abstract mathematical construct that is used for modeling a real-world problem by dividing the problem into a set of connected nodes. We call each of the nodes a vertex and each of the connections an edge.
What is fundamental theorem of graph theory?
In Graph Theory, Handshaking Theorem states in any given graph, Sum of degree of all the vertices is twice the number of edges contained in it. The sum of degree of all the vertices is always even. The sum of degree of all the vertices with odd degree is always even.
What is a simple graph in graph theory?
A simple graph is a graph that does not have more than one edge between any two vertices and no edge starts and ends at the same vertex. In other words a simple graph is a graph without loops and multiple edges. Adjacent Vertices. Two vertices are said to be adjacent if there is an edge (arc) connecting them.
What is the fundamental theorem of graph theory?
In Graph Theory, Handshaking Theorem states in any given graph, Sum of degree of all the vertices is twice the number of edges contained in it.
What is a connected acyclic graph?
An acyclic graph is a graph having no graph cycles. A connected acyclic graph is known as a tree, and a possibly disconnected acyclic graph is known as a forest (i.e., a collection of trees). The numbers of acyclic graphs (forests) on. , 2, are 1, 2, 3, 6, 10, 20, 37, 76, 153.