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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 mathematics and computer science, graph theory is the study of graphs, ... a decomposition of a regular graph into regular subgraphs of given degrees; Graph classes
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.
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).
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 the mathematical discipline of graph theory, the 2-factor theorem, discovered by Julius Petersen, is one of the earliest works in graph theory. It can be stated as follows: [ 1 ] Let G {\displaystyle G} be a regular graph whose degree is an even number, 2 k {\displaystyle 2k} .
Snark (graph theory) Strongly regular graph; Sudoku graph; Supersingular isogeny graph; Suzuki graph; Sylvester graph; Symmetric graph; Szekeres snark; T. Table of ...
The hemi-dodecahedron is a regular map produced by pentagonal embedding of the Petersen graph in the projective plane. The p-hosohedron is a regular map of type {2,p}. The Dyck map is a regular map of 12 octagons on a genus-3 surface. Its underlying graph, the Dyck graph, can also form a regular map of 16 hexagons in a torus.