Configuration graphs are a theoretical tool used in computational complexity theory to prove a relation between graph reachability and complexity classes...

of points and lines in an incidence geometry or a projective configuration, we form a graph with one vertex per point, one vertex per line, and an edge...

Petersen graph is "a remarkable configuration that serves as a counterexample to many optimistic predictions about what might be true for graphs in general...

corresponding points of the other. It is the Levi graph of the Desargues configuration. This configuration consists of ten points and ten lines describing...

is a Turing machine which has a configuration graph that is undirected (that is, configuration i yields configuration j if and only if j yields i). Formally...

In network science, the Configuration Model is a family of random graph models designed to generate networks from a given degree sequence. Unlike simpler...

duality, the same configuration results. Graphs associated with the Desargues configuration include the Desargues graph (its graph of point-line incidences)...

the generalized quadrangle W2 (known as the Cremona–Richmond configuration). The graph is named after William Thomas Tutte and H. S. M. Coxeter; it was...

knowledge graph is a knowledge base that uses a graph-structured data model or topology to represent and operate on data. Knowledge graphs are often used...

graph, the user can follow how the graph evolves, seeing it unfold from a tangled mess into a good-looking configuration. In some interactive graph drawing...

particular graph is a connected cubic graph (regular of degree 3), has girth 6 and each part contains 7 vertices. It is the Heawood graph, the unique...

removed and the remaining graph four-colored, then the coloring can be modified in such a way that when the configuration is re-added, the four-coloring...

the Möbius–Kantor configuration. The Möbius–Kantor graph derives its name from being the Levi graph of the Möbius–Kantor configuration. It has one vertex...

a graph, the robots correspond to particles, and successful navigation corresponds to a path in the configuration space of that graph. For any graph Γ...

counterexample in the theory of visibility graphs and in graph drawing. One way of constructing the Perles configuration is to start with a regular pentagon...

3-edges. It is also the dual configuration of complete bipartite graph, K3,3, called the utility graph (or Thomsen graph), (63 92) or [ 6 3 2 9 ] {\displaystyle...

In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets...

computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context...

] > 0 {\textstyle \mathbb {E} [k^{2}]-2\mathbb {E} [k]>0} , the configuration graph contains the giant connected component, which has infinite size....

girth of the corresponding bipartite graph (the Levi graph of the configuration) must be at least six. A configuration in the plane is denoted by (pγ ℓπ)...

initial configuration of n pebbles on the graph, it is possible, after a possibly-empty series of pebbling moves, to reach a new configuration in which...

Möbius–Kantor configuration is the unique (83). Each incidence structure C corresponds to a bipartite graph called the Levi graph or incidence graph of the structure...

pairs of points. The Levi graph of the Pappus configuration is known as the Pappus graph. It is a bipartite symmetric cubic graph with 18 vertices and 27...

Möbius–Kantor configuration is the unique projective configuration of type (8383). The Möbius–Kantor graph derives its name from being the Levi graph of the...

Grünbaum. The Levi graph of the configuration is the Kronecker cover of the odd graph O4, and is isomorphic to the middle layer graph of the seven-dimensional...

In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability...

quadratic equations. Cayley configuration spaces have a close relationship to the flattenability and combinatorial rigidity of graphs. Definition via linkages...

In graph theory, the strong perfect graph theorem is a forbidden graph characterization of the perfect graphs as being exactly the graphs that have neither...

planar graph with eight vertices and twelve edges. The graph Q4 is the Levi graph of the Möbius configuration. It is also the knight's graph for a toroidal...

projective configuration: each point has exactly three lines through it, and each line has exactly three points on it. The Gray graph is the Levi graph of this...