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A complete graph is a graph in which each pair of graph vertices is connected by an edge. The complete graph with n graph vertices is denoted K_n and has (n; 2)=n (n-1)/2 (the triangular numbers) undirected edges, where (n; k) is a binomial coefficient.
In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge. A complete digraph is a directed graph in which every pair of distinct vertices is connected by a pair of unique edges (one in each direction).
- 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.
Mar 1, 2023 · A complete graph is an undirected graph in which every pair of distinct vertices is connected by a unique edge. In other words, every vertex in a complete graph is adjacent to all other vertices. A complete graph is denoted by the symbol K_n, where n is the number of vertices in the graph.
Nov 21, 2023 · In this lesson, learn about the properties of a complete graph. Moreover, discover a complete graph definition and calculate the vertices, edges, and degree of a complete graph....
- A complete graph is a graph in which every pair of distinct vertices are connected by a unique edge. That is, every vertex is connected to every ot...
- A graph is complete if and only if every pair of vertices is connected by a unique edge. If there are two vertices that are not connected by an edg...
- A graph that is not complete is any graph where two vertices are present but are not connected by an edge. A complete graph requires that every pai...
Jul 12, 2021 · Definition: Complete Graph. A (simple) graph in which every vertex is adjacent to every other vertex, is called a complete graph. If this graph has \(n\) vertices, then it is denoted by \(K_n\). The notation \(K_n\) for a complete graph on \(n\) vertices comes from the name of Kazimierz Kuratowski, a Polish mathematician who lived from 1896–1980.
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from class: Extremal Combinatorics. Definition. A complete graph is a type of graph in which every pair of distinct vertices is connected by a unique edge. This structure is fundamental in graph theory and provides a framework for exploring various concepts related to graph connectivity, extremal properties, and saturation problems.
