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A graph with a loop on vertex 1. In graph theory, a loop (also called a self-loop or a buckle) is an edge that connects a vertex to itself. A simple graph contains no loops. Depending on the context, a graph or a multigraph may be defined so as to either allow or disallow the presence of loops (often in concert with allowing or disallowing ...
Each vertex is assigned to a parallel entity. This vertex centric approach might only work well if the graph depth is very low. Graph depth in BFS is defined as the maximum distance of any vertex in the graph to the source vertex. Therefore, the vertex centric approach is well-suited for GPUs if every thread is mapped to exactly one vertex. [3]
In graph theory and theoretical computer science, the longest path problem is the problem of finding a simple path of maximum length in a given graph.A path is called simple if it does not have any repeated vertices; the length of a path may either be measured by its number of edges, or (in weighted graphs) by the sum of the weights of its edges.
Vertex coloring is often used to introduce graph coloring problems, since other coloring problems can be transformed into a vertex coloring instance. For example, an edge coloring of a graph is just a vertex coloring of its line graph, and a face coloring of a plane graph is just a vertex coloring of its dual. However, non-vertex coloring ...
One may recover the surface itself by gluing a topological disk to the ribbon graph along each boundary component. The partition of the surface into vertex disks, edge disks, and face disks given by the ribbon graph and this gluing process is a different but related representation of the embedding called a band decomposition. [5] The surface ...
That is, it consists of vertices and edges (also called arcs), with each edge directed from one vertex to another, such that following those directions will never form a closed loop. A directed graph is a DAG if and only if it can be topologically ordered, by arranging the vertices as a linear ordering that is consistent with all edge ...
Create a forest (a set of trees) initially consisting of a separate single-vertex tree for each vertex in the input graph. Sort the graph edges by weight. Loop through the edges of the graph, in ascending sorted order by their weight. For each edge: Test whether adding the edge to the current forest would create a cycle.
The problem of graph exploration can be seen as a variant of graph traversal. It is an online problem, meaning that the information about the graph is only revealed during the runtime of the algorithm. A common model is as follows: given a connected graph G = (V, E) with non-negative edge weights. The algorithm starts at some vertex, and knows ...