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Regular graphs of degree at most 2 are easy to classify: a 0-regular graph consists of disconnected vertices, a 1-regular graph consists of disconnected edges, and a 2-regular graph consists of a disjoint union of cycles and infinite chains. A 3-regular graph is known as a cubic 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).
Every strongly regular graph with = is a geodetic graph, a graph in which every two vertices have a unique unweighted shortest path. [6] The only known strongly regular graphs with μ = 1 {\displaystyle \mu =1} are those where λ {\displaystyle \lambda } is 0, therefore triangle-free as well.
In the mathematical field of graph theory, a distance-regular graph is a regular graph such that for any two vertices v and w, the number of vertices at distance j from v and at distance k from w depends only upon j, k, and the distance between v and w. Some authors exclude the complete graphs and disconnected graphs from this definition.
In a regular graph, every vertex has the same degree, and so we can speak of the degree of the graph. A complete graph (denoted K n {\displaystyle K_{n}} , where n {\displaystyle n} is the number of vertices in the graph) is a special kind of regular graph where all vertices have the maximum possible degree, n − 1 {\displaystyle n-1} .
An undirected graph with three vertices and three edges. In one restricted but very common sense of the term, [1] [2] a graph is an ordered pair = (,) comprising: , a set of vertices (also called nodes or points);
K n has n(n – 1)/2 edges (a triangular number), and is a regular graph of degree n – 1. All complete graphs are their own maximal cliques. 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.
Pages in category "Regular graphs" The following 119 pages are in this category, out of 119 total. This list may not reflect recent changes. * Regular graph; 0–9.