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16 relations: Algorithm, Approximation algorithm, Degree (graph theory), Eulerian path, Hamiltonian path, Handshaking lemma, Induced subgraph, Matching (graph theory), Metric space, Minimum spanning tree, Multigraph, Path (graph theory), Pseudocode, Shortest path problem, Travelling salesman problem, Triangle inequality.
Algorithm
In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.
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Approximation algorithm
In computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to NP-hard optimization problems with provable guarantees on the distance of the returned solution to the optimal one.
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Degree (graph theory)
In graph theory, the degree (or valency) of a vertex of a graph is the number of edges incident to the vertex, with loops counted twice.
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Eulerian path
In graph theory, an Eulerian trail (or Eulerian path) is a trail in a finite graph which visits every edge exactly once.
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Hamiltonian path
In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once.
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Handshaking lemma
In graph theory, a branch of mathematics, the handshaking lemma is the statement that every finite undirected graph has an even number of vertices with odd degree (the number of edges touching the vertex).
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Induced subgraph
In graph theory, an induced subgraph of a graph is another graph, formed from a subset of the vertices of the graph and all of the edges connecting pairs of vertices in that subset.
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Matching (graph theory)
In the mathematical discipline of graph theory, a matching or independent edge set in a graph is a set of edges without common vertices.
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Metric space
In mathematics, a metric space is a set for which distances between all members of the set are defined.
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Minimum spanning tree
A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted (un)directed graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight.
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Multigraph
In mathematics, and more specifically in graph theory, a multigraph (in contrast to a simple graph) is a graph which is permitted to have multiple edges (also called parallel edges), that is, edges that have the same end nodes.
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Path (graph theory)
In graph theory, a path in a graph is a finite or infinite sequence of edges which connect a sequence of vertices which, by most definitions, are all distinct from one another.
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Pseudocode
Pseudocode is an informal high-level description of the operating principle of a computer program or other algorithm.
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Shortest path problem
In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.
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Travelling salesman problem
The travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city and returns to the origin city?" It is an NP-hard problem in combinatorial optimization, important in operations research and theoretical computer science.
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Triangle inequality
In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.
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