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2. Line graph - Wikipedia

   en.wikipedia.org/wiki/Line_graph

   Line graph. In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L (G) that represents the adjacencies between edges of G. L (G) is constructed in the following way: for each edge in G, make a vertex in L (G); for every two edges in G that have a vertex in common, make an edge between their ...

3. Graph theory - Wikipedia

   en.wikipedia.org/wiki/Graph_theory

   A drawing of a graph. In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called arcs, links or lines ).

4. Perfect graph - Wikipedia

   en.wikipedia.org/wiki/Perfect_graph

   Perfect graph. The graph of the 3-3 duoprism (the line graph of ) is perfect. Here it is colored with three colors, with one of its 3-vertex maximum cliques highlighted. In graph theory, a perfect graph is a graph in which the chromatic number equals the size of the maximum clique, both in the graph itself and in every induced subgraph.

5. Line graph of a hypergraph - Wikipedia

   en.wikipedia.org/wiki/Line_graph_of_a_hypergraph

   In graph theory, particularly in the theory of hypergraphs, the line graph of a hypergraph H, denoted L (H), is the graph whose vertex set is the set of the hyperedges of H, with two vertices adjacent in L (H) when their corresponding hyperedges have a nonempty intersection in H. In other words, L (H) is the intersection graph of a family of ...

6. Graph (discrete mathematics) - Wikipedia

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

   A graph with six vertices and seven edges. In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some sense "related". The objects are represented by abstractions called vertices (also called nodes or points) and each of the related pairs of vertices ...

7. Graph isomorphism - Wikipedia

   en.wikipedia.org/wiki/Graph_isomorphism

   A set of graphs isomorphic to each other is called an isomorphism class of graphs. The question of whether graph isomorphism can be determined in polynomial time is a major unsolved problem in computer science, known as the graph isomorphism problem. [1] [2] The two graphs shown below are isomorphic, despite their different looking drawings.

8. Connectivity (graph theory) - Wikipedia

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

   This graph becomes disconnected when the right-most node in the gray area on the left is removed This graph becomes disconnected when the dashed edge is removed.. In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more ...

9. Split graph - Wikipedia

   en.wikipedia.org/wiki/Split_graph

   Split graph. A split graph, partitioned into a clique and an independent set. In graph theory, a branch of mathematics, a split graph is a graph in which the vertices can be partitioned into a clique and an independent set. Split graphs were first studied by Földes and Hammer ( 1977a, 1977b ), and independently introduced by Tyshkevich and ...