Complete graph geeksforgeeks A clique is a complete subgraph of a graph. Definition of Graph A graph is a mathematical structure used to represent a set of objects and the connections between them: The objects are called Jul 12, 2025 · Your All-in-One Learning Portal: GeeksforGeeks is a comprehensive educational platform that empowers learners across domains-spanning computer science and programming, school education, upskilling, commerce, software tools, competitive exams, and more. Jul 26, 2025 · If a graph contains a Hamiltonian cycle, it is called Hamiltonian graph otherwise it is non-Hamiltonian. Graph Theory Basics A graph is a Sep 15, 2025 · Graph Theory is a branch of mathematics concerned with the study of objects (called vertices or nodes) and the connections between them (called edges). S A complete graph is a type of graph in which every pair of distinct vertices is connected by a unique 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. Finding a Hamiltonian Cycle in a graph is a well-known NP-complete problem, which means that there's no known efficient algorithm to solve it for all types of graphs. Fig. Jul 23, 2025 · Graph theory is a branch of mathematics that studies the properties and applications of graphs. 3. A graph is a collection of various vertices, also known as nodes, and these nodes are connected via edges. Complete graph A complete graph is a simple graph in which every pair of vertices is joined by an edge. Graphs are common in computer science, network analysis, and many other everyday uses because they provide a good representation of connection, relationship, and process. 15 shows five complete graphs with their number of vertices varying from 1 to 5. May 26, 2025 · Graph theory is a basic branch of discrete mathematics that mainly focuses on the relationship between objects. [1] Graph theory itself is typically dated as beginning with Leonhard Euler 's 1736 work on Graphs are an important Data Structure in Computer Science and are used to represent and model many types of relationships and connections between objects. Jul 23, 2025 · Graph coloring is a fundamental concept in graph theory, and the chromatic number is a key parameter that quantifies the coloring properties of a graph. Oct 27, 2025 · Your All-in-One Learning Portal: GeeksforGeeks is a comprehensive educational platform that empowers learners across domains-spanning computer science and programming, school education, upskilling, commerce, software tools, competitive exams, and more. 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. Jul 23, 2025 · Your All-in-One Learning Portal: GeeksforGeeks is a comprehensive educational platform that empowers learners across domains-spanning computer science and programming, school education, upskilling, commerce, software tools, competitive exams, and more. In older literature, complete graphs are sometimes called universal graphs. Any complete graph of n vertices is denoted by Kn. These graphs help us model and solve problems in computer science, engineering, biology, logistics, and many other fields. Jul 12, 2025 · Given an undirected graph with N nodes and E edges and a value K, the task is to print all set of nodes which form a K size clique. In this article, we will discuss all the Sep 2, 2022 · Your All-in-One Learning Portal: GeeksforGeeks is a comprehensive educational platform that empowers learners across domains-spanning computer science and programming, school education, upskilling, commerce, software tools, competitive exams, and more. Mar 1, 2023 · Your All-in-One Learning Portal: GeeksforGeeks is a comprehensive educational platform that empowers learners across domains-spanning computer science and programming, school education, upskilling, commerce, software tools, competitive exams, and more. 15. Aug 25, 2025 · Graph Theory is a branch of mathematics that deals with graphs—structures made up of vertices (points) and edges (lines). Sep 29, 2025 · Your All-in-One Learning Portal: GeeksforGeeks is a comprehensive educational platform that empowers learners across domains-spanning computer science and programming, school education, upskilling, commerce, software tools, competitive exams, and more. . Figure 3. However, it can be solved for small or specific types of graphs. These objects are called vertices and these vertices are joined by edges. Jan 24, 2023 · Your All-in-One Learning Portal: GeeksforGeeks is a comprehensive educational platform that empowers learners across domains-spanning computer science and programming, school education, upskilling, commerce, software tools, competitive exams, and more. Five complete graphs. Let's go into the introductory aspects of the chromatic number. 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). In other words, in a complete graph, every vertex is adjacent to every other vertex. A graph is a collection of vertices (also called nodes) connected by edges (also called links). Graphs are used to model pairwise relations between objects, making them a powerful tool for representing and analyzing complex systems in various fields. Jul 15, 2025 · Your All-in-One Learning Portal: GeeksforGeeks is a comprehensive educational platform that empowers learners across domains-spanning computer science and programming, school education, upskilling, commerce, software tools, competitive exams, and more. A complete graph is a graph in which each pair of graph vertices is connected by an edge. daye nwsom jrcwv ejd gunwfe dniuh jlbvsj vxuzxnn ndpqj wybds ohwxg ggfoc yxcj xfbhr wqeu