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A simple graph contains no double edges or loops. [1] The degree sequence is a list of numbers in nonincreasing order indicating the number of edges incident to each vertex in the graph. [2] If a simple graph exists for exactly the given degree sequence, the list of integers is called graphic. The Havel-Hakimi algorithm constructs a special ...
Graph. Worst-case performance. Tarjan's strongly connected components algorithm is an algorithm in graph theory for finding the strongly connected components (SCCs) of a directed graph. It runs in linear time, matching the time bound for alternative methods including Kosaraju's algorithm and the path-based strong component algorithm.
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. The problem of finding the shortest path between two intersections on a road map may be modeled as a special case of the shortest path problem in graphs ...
This graph becomes disconnected when the right-most node in the gray area on the left is removed This graph becomes disconnected when the dashed edge is removed.. In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more ...
Grundy number. An optimal greedy coloring (left) and Grundy coloring (right) of a crown graph. The numbers indicate the order in which the greedy algorithm colors the vertices. In graph theory, the Grundy number or Grundy chromatic number of an undirected graph is the maximum number of colors that can be used by a greedy coloring strategy that ...
Greedy coloring. Two greedy colorings of the same crown graph using different vertex orders. The right example generalises to 2-colorable graphs with n vertices, where the greedy algorithm expends n/2 colors. In the study of graph coloring problems in mathematics and computer science, a greedy coloring or sequential coloring [1] is a coloring ...
In graph theory, the blossom algorithm is an algorithm for constructing maximum matchings on graphs. The algorithm was developed by Jack Edmonds in 1961, [1] and published in 1965. [2] Given a general graph G = (V, E), the algorithm finds a matching M such that each vertex in V is incident with at most one edge in M and |M| is maximized.
Graph isomorphism. In graph theory, an isomorphism of graphs G and H is a bijection between the vertex sets of G and H. such that any two vertices u and v of G are adjacent in G if and only if and are adjacent in H. This kind of bijection is commonly described as "edge-preserving bijection", in accordance with the general notion of isomorphism ...