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  2. Shannon multigraph - Wikipedia

    en.wikipedia.org/wiki/Shannon_multigraph

    In the mathematical discipline of graph theory, Shannon multigraphs, named after Claude Shannon by Vizing (1965), are a special type of triangle graphs, which are used in the field of edge coloring in particular. A Shannon multigraph is multigraph with 3 vertices for which either of the following conditions holds:

  3. Graph theory - Wikipedia

    en.wikipedia.org/wiki/Graph_theory

    A loop is an edge that joins a vertex to itself. Graphs as defined in the two definitions above cannot have loops, because a loop joining a vertex to itself is the edge (for an undirected simple graph) or is incident on (for an undirected multigraph) {,} = {} which is not in {{,},}. To allow loops, the definitions must be expanded.

  4. Triangle-free graph - Wikipedia

    en.wikipedia.org/wiki/Triangle-free_graph

    In the mathematical area of graph theory, a triangle-free graph is an undirected graph in which no three vertices form a triangle of edges. Triangle-free graphs may be equivalently defined as graphs with clique number ≤ 2, graphs with girth ≥ 4, graphs with no induced 3-cycle , or locally independent graphs.

  5. Signed graph - Wikipedia

    en.wikipedia.org/wiki/Signed_graph

    In the area of graph theory in mathematics, a signed graph is a graph in which each edge has a positive or negative sign. A signed graph is balanced if the product of edge signs around every cycle is positive. The name "signed graph" and the notion of balance appeared first in a mathematical paper of Frank Harary in 1953. [1]

  6. Euclidean minimum spanning tree - Wikipedia

    en.wikipedia.org/wiki/Euclidean_minimum_spanning...

    For each remaining edge, the vertices of the Delaunay triangles that use that edge cannot lie within the empty lune of the relative neighborhood graph. Because the empty-region criteria for these graphs are progressively weaker, these graphs form an ordered sequence of subgraphs. That is, using "⊆" to denote the subset relationship among ...

  7. Bipartite graph - Wikipedia

    en.wikipedia.org/wiki/Bipartite_graph

    A hypergraph is a combinatorial structure that, like an undirected graph, has vertices and edges, but in which the edges may be arbitrary sets of vertices rather than having to have exactly two endpoints. A bipartite graph (,,) may be used to model a hypergraph in which U is the set of vertices of the hypergraph, V is the set of hyperedges, and ...

  8. Point-set triangulation - Wikipedia

    en.wikipedia.org/wiki/Point-set_triangulation

    The Delaunay triangulation of a set of points in the plane contains the Gabriel graph, the nearest neighbor graph and the minimal spanning tree of . Triangulations have a number of applications, and there is an interest to find the "good" triangulations of a given point set under some criteria as, for instance minimum-weight triangulations .

  9. Homeomorphism (graph theory) - Wikipedia

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

    In general, a subdivision of a graph G (sometimes known as an expansion [2]) is a graph resulting from the subdivision of edges in G. The subdivision of some edge e with endpoints {u,v } yields a graph containing one new vertex w, and with an edge set replacing e by two new edges, {u,w } and {w,v }. For directed edges, this operation shall ...

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