In the mathematical field of graph theory, the Chang graphs are three 12-regular undirected graphs, each with 28 vertices and 168 edges. They are strongly...

a line graph have been studied, including line graphs of line graphs, line graphs of multigraphs, line graphs of hypergraphs, and line graphs of weighted...

Graph neural networks (GNN) are specialized artificial neural networks that are designed for tasks whose inputs are graphs. One prominent example is molecular...

that such a graph is perfect." Trivially perfect graphs are also known as comparability graphs of trees, arborescent comparability graphs, and quasi-threshold...

arc-transitive graphs are strongly regular. A strongly regular graph is called primitive if both the graph and its complement are connected. All the above graphs are...

most 3n maximal cliques. The graphs meeting this bound are the Moon–Moser graphs K3,3,..., a special case of the Turán graphs arising as the extremal cases...

coloring. Explicit, though large, graphs with high girth and chromatic number can be constructed as certain Cayley graphs of linear groups over finite fields...

various individual (finite) graphs. The columns 'vertices', 'edges', 'radius', 'diameter', 'girth', 'P' (whether the graph is planar), χ (chromatic number)...

each other in the cycle. Strongly chordal graphs have a forbidden subgraph characterization as the graphs that do not contain an induced cycle of length...

Knight's graph Queen's graph Rook's graph Bishop's graph Lattice graph Chess portal Chang, Gerard J. (1998), "Algorithmic aspects of domination in graphs", in...

the maximum clique can be found in even-hole-free graphs in polynomial time. "even-cycle--free graphs", www.graphclasses.org, retrieved 2023-03-12 Conforti...

bipartition of G. Map graphs are the half-squares of planar graphs, and halved cube graphs are the half-squares of hypercube graphs. Leaf powers are the...

path problem can be defined for graphs whether undirected, directed, or mixed. The definition for undirected graphs states that every edge can be traversed...

a graph", Theory of Graphs (Internat. Sympos., Rome, 1966), New York: Gordon and Breach, pp. 349–355, MR 0223271. Wang, Tao-Ming; Yang, Cheng-Chang; Hsu...

graphs, where there only exist one type of nodes and edges. However, the theory and methods for heterophily on heterogeneous graphs, temporal graphs and...

traversal. Pseudoforests and grid graphs also have queue number 1. Outerplanar graphs have queue number at most 2; the 3-sun graph (a triangle with each of its...

In graph theory, the planar separator theorem is a form of isoperimetric inequality for planar graphs, that states that any planar graph can be split...

undirected graphs formed by the edges and vertices of three-dimensional convex polyhedra: they are exactly the 3-vertex-connected planar graphs. That is...

which gives a linear run-time for dense graphs. There are other algorithms that work in linear time on dense graphs. If the edge weights are integers represented...

knowledge graph's entities and relations while preserving their semantic meaning. Leveraging their embedded representation, knowledge graphs (KGs) can...

sovereignty of the monarchs over subjugated polities. According to Ruth H. Chang, continuation of Shang religion also provided opportunities to further share...

language of graphs.) The theory of random graphs is ω categorical, complete, and decidable, and its countable model is called the Rado graph. A statement...

graph is created, subgraphs can be vectorized, stored in a vector database, and used for retrieval as in plain RAG. The advantage here is that graphs...

graph but cannot be drawn without crossings on a plane. Another family of graphs that can be embedded on the Möbius strip, but not on the plane, are the...

BERT was originally published by Google researchers Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. The design has its origins from pre-training...

Applications. Academic Press. pp. 92–93. ISBN 0-12-530985-6. Maki LR, Galyan EL, Chang-Chien MM, Caldwell DR (September 1974). "Ice nucleation induced by pseudomonas...

in China in containing sequences of graphs; shards were found with horizontal sequences of 12, 7, 5 and 4 graphs, suggesting that they may be a form of...

syndrome - Symptoms and causes". Mayo Clinic. Retrieved December 5, 2023. Chang L (March 2011). "The role of stress on physiologic responses and clinical...

In the case of dense graphs the time bound becomes O ( | V | 2.5 ) {\displaystyle O(|V|^{2.5})} , and for sparse random graphs it runs in time O ( |...

in graphical shape (字形; zìxíng), the "external appearances of individual graphs", and in graphical form (字体; 字體; zìtǐ), "overall changes in the distinguishing...