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A graph with 6 vertices and 7 edges where the vertex number 6 on the far-left is a leaf vertex or a pendant vertex. In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph ...
A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).
Calculus on finite weighted graphs is used in a wide range of applications from different fields such as image processing, machine learning, and network analysis. A non-exhaustive list of tasks in which finite weighted graphs have been employed is: image denoising [2] [3] image segmentation [4] image inpainting [2] [5] tomographic ...
The algorithm operates by building this tree one vertex at a time, from an arbitrary starting vertex, at each step adding the cheapest possible connection from the tree to another vertex. The algorithm was developed in 1930 by Czech mathematician Vojtěch Jarník [ 1 ] and later rediscovered and republished by computer scientists Robert C. Prim ...
For each vertex in , we locate the first vertex in reachable by , and the last vertex in that reaches to . That is, we are looking at how early into Q {\displaystyle Q} we can get from v {\displaystyle v} , and how far we can stay in Q {\displaystyle Q} and still get back to v {\displaystyle v} .
In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges of G. L(G) is constructed in the following way: for each edge in G, make a vertex in L(G); for every two edges in G that have a vertex in common, make an edge between their corresponding vertices in L(G).
A vertex with degree 1 is called a leaf vertex or end vertex or a pendant vertex, and the edge incident with that vertex is called a pendant edge. In the graph on the right, {3,5} is a pendant edge. This terminology is common in the study of trees in graph theory and especially trees as data structures .
In graph theory, an adjacent vertex of a vertex v in a graph is a vertex that is connected to v by an edge.The neighbourhood of a vertex v in a graph G is the subgraph of G induced by all vertices adjacent to v, i.e., the graph composed of the vertices adjacent to v and all edges connecting vertices adjacent to v.
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