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  2. Regular graph - Wikipedia

    en.wikipedia.org/wiki/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]

  3. Graph theory - Wikipedia

    en.wikipedia.org/wiki/Graph_theory

    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

  4. Strongly regular graph - Wikipedia

    en.wikipedia.org/wiki/Strongly_regular_graph

    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.

  5. Regular map (graph theory) - Wikipedia

    en.wikipedia.org/wiki/Regular_map_(graph_theory)

    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.

  6. Graph (discrete mathematics) - Wikipedia

    en.wikipedia.org/wiki/Graph_(discrete_mathematics)

    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).

  7. Szemerédi regularity lemma - Wikipedia

    en.wikipedia.org/wiki/Szemerédi_regularity_lemma

    The edges between parts behave in a "random-like" fashion. In extremal graph theory, Szemerédi’s regularity lemma states that a graph can be partitioned into a bounded number of parts so that the edges between parts are regular (in the sense defined below).

  8. Distance-regular graph - Wikipedia

    en.wikipedia.org/wiki/Distance-regular_graph

    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.

  9. Cubic graph - Wikipedia

    en.wikipedia.org/wiki/Cubic_graph

    The Petersen graph is a cubic graph. The complete bipartite graph, is an example of a bicubic graph. In the mathematical field of graph theory, a cubic graph is a graph in which all vertices have degree three. In other words, a cubic graph is a 3-regular graph. Cubic graphs are also called trivalent graphs.

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