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Regular graph. In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency. A regular directed graph must also satisfy the stronger condition that the indegree and outdegree of each internal vertex are equal to each other. [1]
In graph theory, a strongly regular graph (SRG) is a regular graph G = (V, E) with v vertices and degree k such that for some given integers. every two adjacent vertices have λ common neighbours, and. every two non-adjacent vertices have μ common neighbours. Such a strongly regular graph is denoted by srg (v, k, λ, μ); its "parameters" are ...
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.
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).
Random regular graph. A random r-regular graph is a graph selected from , which denotes the probability space of all r -regular graphs on vertices, where and is even. [1] It is therefore a particular kind of random graph, but the regularity restriction significantly alters the properties that will hold, since most graphs are not regular.
A k-factor of a graph is a spanning k-regular subgraph, and a k-factorization partitions the edges of the graph into disjoint k-factors. A graph G is said to be k-factorable if it admits a k-factorization. In particular, a 1-factor is a perfect matching, and a 1-factorization of a k-regular graph is a proper edge coloring with k colors.
Set Reconstruction Conjecture: Any two graphs on at least four vertices with the same sets of vertex-deleted subgraphs are isomorphic. Given a graph , an edge-deleted subgraph of is a subgraph formed by deleting exactly one edge from . For a graph , the edge-deck of G, denoted , is the multiset of all isomorphism classes of edge-deleted ...
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.