Children: Regular graphs
The Coxeter graph is an important concept in the fields of algebra, geometry, and graph theory. Specifically, it is a particular type of graph that represents the symmetric group and the properties of certain mathematical structures, particularly in relation to Coxeter groups. Here are some key features of the Coxeter graph: 1. **Definition and Structure**: The Coxeter graph is a finite undirected graph with 12 vertices and 18 edges.
A crown graph is a specific type of graph in graph theory. It is denoted as \( C_n \) and is defined as the graph that consists of two cycles \( C_n \) and \( C_{n+1} \) that are connected in a certain way. More formally, a crown graph can be defined as follows: 1. **Vertices**: The crown graph has \( 2n \) vertices, which can be represented as two disjoint cycles.
Cube-connected cycles (CCC) is a network topology used in parallel computing and interconnecting processing elements. It is a hybrid structure that combines features of both the hypercube network and cyclical connections. The primary purpose of CCC is to facilitate efficient communication between multiple processors in a system, making it suitable for parallel processing and distributed computing environments.
A **cubic graph**, also known as a **3-regular graph**, is a type of graph in which every vertex has a degree of exactly three. This means that each vertex is connected to exactly three edges. Cubic graphs are an important class of graphs in graph theory and have various applications in computer science, network design, and combinatorial optimization. ### Properties of Cubic Graphs: 1. **Degree**: Each vertex has a degree of 3.
The term "Dejter graph" might not be widely recognized in the mathematical or graph theory communities. It is possible that it is a misspelling or a less common term. If you are referring to a well-known concept or a specific type of graph, please provide additional context or check the spelling. Some possible related terms could include "De Bruijn graph," "Dijkstra's graph," or "Directed graph," among others.
The Desargues graph is a finite, undirected graph named after the French mathematician Gérard Desargues. It is a special type of combinatorial structure that has connections to projective geometry and graph theory. The Desargues graph can be defined as follows: 1. **Vertices**: The graph has 20 vertices, which can be represented as points in a projective plane of order 2. 2. **Edges**: The graph has 30 edges.
A dipole graph is a specific type of graph used in physics and mathematics to represent a system featuring two opposing charges or poles, typically illustrated in the context of electric or magnetic fields. In the context of electrostatics, for example, a dipole consists of two point charges of equal magnitude and opposite sign separated by a distance.
Double-star snark refers to a specific kind of humor or sarcasm commonly found in the realm of online conversations, particularly in fan communities or discussions about various forms of media such as literature, movies, or video games. The term "snark" itself typically conveys a cutting, witty, or clever form of critique or commentary that can be both humorous and insightful.
A Dyck graph is a type of graph that represents the relationships between different valid sequences of balanced parentheses or paths in a lattice. The concept is often tied to combinatorial structures and is particularly connected to Dyck words, which are sequences of symbols that maintain a balance (for every opening symbol, there is a corresponding closing symbol).
The Dürer graph is a specific type of graph in the field of graph theory, named after the German painter and printmaker Albrecht Dürer. It is a highly symmetrical graph that has 12 vertices and 24 edges. The graph can be represented as a 3-dimensional object, which resembles a cube, and it is known for its interesting geometric properties.
The Ellingham-Horton graph is a thermodynamic reference tool used in metallurgy and materials science. It provides a visual representation of the standard free energy changes (ΔG) of various metal oxides as a function of temperature. Named after the researchers Sir Harold Ellingham and J. H. Horton, the graph is primarily used to analyze the stability of metal oxides and their tendency to reduce (or be reduced to their elemental form) at given temperatures.
The F26A graph is a specific type of graph used in the context of graph theory. It is commonly referenced as a particular standard graph that has a specific structure, often used in discussions of properties such as planarity, connectivity, and colorability. The F26A graph is often denoted within standard graph classifications and may have applications in various mathematical and computational contexts.
"Flower snark" typically refers to a playful or humorous type of sarcasm or witty commentary centered around flowers, gardening, or the aesthetics associated with them. It can manifest in various ways, such as funny social media posts, witty remarks about plant care, or tongue-in-cheek observations about floral design and gardening trends.
The folded cube graph is a type of mathematical graph that can be derived from the hypercube graph, particularly useful in the field of combinatorial design and graph theory. The concept is particularly involved in the analysis of topology, network design, and parallel processing. ### Definition: The \(n\)-dimensional folded cube graph, denoted \(FQ_n\), is constructed from the \(n\)-dimensional hypercube \(Q_n\).
A Folkman graph is a specific type of graph in graph theory named after the mathematician Julian Folkman. It is characterized by its properties related to edge connectivity and its structure. One important aspect of Folkman graphs is that they are used to investigate the relationship between graph properties such as colorings and connectivity. Specifically, Folkman graphs can be employed in studies related to hypergraphs and their extensions, especially in the context of coloring problems in combinatorial mathematics.
A Foster cage is a type of enclosure commonly used in biological research and veterinary settings to house animals. Named after biologist John Foster, these cages are designed to provide a controlled environment for animals, often for purposes such as observation, experimentation, or breeding. Foster cages are typically made from materials that allow for easy cleaning, visibility, and airflow.
The Foster graph is a specific type of graph in the field of graph theory. It is characterized as a bipartite graph with 12 vertices and 18 edges. The vertices can be divided into two disjoint sets, and every edge connects a vertex from one set to a vertex in the other set. The importance of the Foster graph arises from its role in various areas of graph theory, such as in the study of graph properties and structures, including colorability and chromatic polynomials.
The Franklin graph is a specific type of mathematical graph named after the American polymath Benjamin Franklin. It is notable for being a 12-vertex, 18-edge graph that can be geometrically embedded in three-dimensional space without any edges crossing. The Franklin graph is often used in the study of topology and graph theory due to its interesting properties. One of the notable features of the Franklin graph is its connectivity; it is 3-connected, meaning that removing any two vertices will not disconnect the graph.