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Two vertices (or edges) of a periodic graph are symmetric if they are in the same orbit of the symmetry group of the graph; in other words, two vertices (or edges) are symmetric if there is a symmetry of the net that moves one onto the other. In chemistry, there is a tendency to refer to orbits of vertices or edges as “kinds” of vertices or ...
An adjacency list representation for a graph associates each vertex in the graph with the collection of its neighbouring vertices or edges. There are many variations of this basic idea, differing in the details of how they implement the association between vertices and collections, in how they implement the collections, in whether they include both vertices and edges or only vertices as first ...
Multiple edges, not allowed under the definition above, are two or more edges with both the same tail and the same head. In one more general sense of the term allowing multiple edges, [5] a directed graph is an ordered triple = (,,) comprising: , a set of vertices (also called nodes or points);
In chemical graph theory and in mathematical chemistry, a molecular graph or chemical graph is a representation of the structural formula of a chemical compound in terms of graph theory. A chemical graph is a labeled graph whose vertices correspond to the atoms of the compound and edges correspond to chemical bonds.
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.
They are maximally connected as the only vertex cut which disconnects the graph is the complete set of vertices. The complement graph of a complete graph is an empty graph. If the edges of a complete graph are each given an orientation, the resulting directed graph is called a tournament. K n can be decomposed into n trees T i such that T i has ...
A gear graph, denoted G n, is a graph obtained by inserting an extra vertex between each pair of adjacent vertices on the perimeter of a wheel graph W n. Thus, G n has 2n+1 vertices and 3n edges. [4] Gear graphs are examples of squaregraphs, and play a key role in the forbidden graph characterization of squaregraphs. [5]
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).