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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 directed graph with three vertices and four directed edges (the double arrow represents an edge in each direction). A directed graph or digraph is a graph in which edges have orientations. In one restricted but very common sense of the term, [5] a directed graph is an ordered pair = (,) comprising:
This sortable list points to the articles describing various individual (finite) graphs. [1] The columns 'vertices', 'edges', ' radius ', ' diameter ', ' girth ', 'P' (whether the graph is planar ), χ ( chromatic number ) and χ' ( chromatic index ) are also sortable, allowing to search for a parameter or another.
The two edges along the cycle adjacent to any of the vertices are not written down. Let v be the vertices of the graph and describe the Hamiltonian circle along the p vertices by the edge sequence v 0 v 1, v 1 v 2, ...,v p−2 v p−1, v p−1 v 0. Halting at a vertex v i, there is one unique vertex v j at a distance d i joined by a chord with v i,
Let G be a simple plane graph with n vertices; we may add edges if necessary so that G is a maximally plane graph. If n < 3, the result is trivial. If n ≥ 3, then all faces of G must be triangles, as we could add an edge into any face with more sides while preserving planarity, contradicting the assumption of maximal planarity.
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.
Differential equations or difference equations on such graphs can be employed to leverage the graph's structure for tasks such as image segmentation (where the vertices represent pixels and the weighted edges encode pixel similarity based on comparisons of Moore neighborhoods or larger windows), data clustering, data classification, or ...
In the mathematical field of graph theory, the Gray graph is an undirected bipartite graph with 54 vertices and 81 edges. It is a cubic graph : every vertex touches exactly three edges. It was discovered by Marion C. Gray in 1932 (unpublished), then discovered independently by Bouwer 1968 in reply to a question posed by Jon Folkman 1967.