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- Finite Graphs. A graph is said to be finite if it has a finite number of vertices and a finite number of edges. A finite graph is a graph with a finite number of vertices and edges.
- Infinite Graph: A graph is said to be infinite if it has an infinite number of vertices as well as an infinite number of edges.
- Trivial Graph: A graph is said to be trivial if a finite graph contains only one vertex and no edge. A trivial graph is a graph with only one vertex and no edges.
- Simple Graph: A simple graph is a graph that does not contain more than one edge between the pair of vertices. A simple railway track connecting different cities is an example of a simple graph.
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Aug 3, 2023 · In graph theory, a trivial graph is the simplest and most basic type of graph that exists. It consists of just one vertex (node) and no edges. This means that a trivial graph contains only a single point without any connections to other points, as there are no edges to link it to other vertices.
- Directed Graph in Graph Theory
- Undirected Graph in Graph Theory
- Null Graph in Graph Theory
- Trivial Graph in Graph Theory
- Simple Graph in Graph Theory
- Complete Graph in Graph Theory
- Connected Graph in Graph Theory
- Disconnected Graph in Graph Theory
- Regular Graph in Graph Theory
- Cyclic Graph in Graph Theory
A graph whose all edges are directed by arrows is known as a directed graph. They are also known as digraphs. In the above image, we can see a directed graph where all the edges are directed in a certain direction.
A graph whose edges are not directed by arrows is known as an undirected graph. In the above image, we see an undirected graph as its edges are not marked by arrows.
A graph in which there are no edges between its vertices is known as a null graph. It is also called an empty graph. A null graph with n number of vertices is denoted by NnNn. In the above image, three different null graphs are shown.
A graph with only one vertex is known as a trivial graph. In the above image, we see only one node and edges arising from it, thus it is a trivial graph.
A graph that is undirected and has no parallel edges orloopsis known as a simple graph. A simple graph with nvertices has the degree of every vertex is at most n-1. In the above image, we can see the difference between a simple and not a simple graph.
A graph in which every pair of vertices is joined by only one edge is called a completegraph. It contains all the possible edges. A complete graph with n number of vertices contains exactly nC2nC2 edges and is represented by KnKn. In the above image we see that each vertex in the graph is connected with all the remaining vertices through exactly on...
A connected graph is a graph where we can visit from any one vertex to any other vertex. In a connected graph, there is at least one edge or path that exists between every pair of vertices. In the above image we can traverse from any one vertex to any other vertex; it is a connected graph.
A disconnected graph is a graph in which no path exists between every pair of vertices. In the above image we see disconnected graphs.
A Regular graph is a graph in which the degree of all the vertices is the same. If the degree of all the vertices is k, then it is called a k-regular graph. In the above image all the vertices have degree 2 and thus it is a 2-regular graph.
A graph with n vertices and n edges forming a cycle of nwith all its edges is known as cycle graph. Any graph containing at least one cycle in it is known as a cyclic graph. In the above image the graph contains two cycles in it hence it is a cyclic graph.
math.mit.edu · research · highschoolGraph Theory and the Six Degrees of Separation - MIT Mathematics
In this paper, we will introduce the basics of graph theory and learn how it is applied to networks through the study of random graphs, which links the subjects of graph theory and probability together. We will also explore and analyze the concept of the six degrees of separation and how random graphs can be applied to social networks.
The cycle graph of order n 3, denoted by Cn = (V; E), is the graph that has as a set of edges E = fx1x2; x2x3; : : : ; xn 1xn; xnx1g. 1g [ fxnx1; xnx2; : : : ; xnxn 1g. Let r and s be positive integers. A graph is r-regular if all vertices have degree r. A graph G = (V; E) is bipartite if there are two non-empty subsets V1 and V2 such that.
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Trivial Graph. A graph with only one vertex is called a Trivial Graph. Example. In the above shown graph, there is only one vertex ‘a’ with no other edges. Hence it is a Trivial graph. Explore our latest online courses and learn new skills at your own pace. Enroll and become a certified expert to boost your career. Non-Directed Graph.
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Feb 20, 2023 · Definition. The graph with no vertices and no edges is the null graph. A graph with one vertex is a trivial graph. Graphs other than the null graph and the trivial graphs are nontrivial graphs. Note 1.1.A. We’ll often abbreviate a simple graph as (V,E) where V is the vertex set and Eis a set of two-element subsets of V. In this way we can ...
