A **strongly chordal graph** is a specific type of graph that combines properties of both chordal graphs and certain restrictions on the structure of its cliques. 1. **Chordal Graph**: A graph is defined as chordal (or "circular" or "perfectly triangulated") if every cycle of four or more vertices has a chord. A chord is an edge that is not part of the cycle but connects two vertices of the cycle.

A **triangle-free graph** is a type of graph that does not contain any cycles of length three, which means it does not have any set of three vertices that are mutually connected by edges. In other words, if you pick any three vertices in the graph, at least one pair of those vertices will not be directly connected by an edge. Triangle-free graphs can be characterized using graph theory, and they have significant implications in various areas, including combinatorics, algorithm design, and social networks.

A graph is said to be **well-covered** if all of its maximal independent sets are of the same size. An independent set of a graph is a set of vertices no two of which are adjacent. A maximal independent set is an independent set that cannot be extended by including any adjacent vertex.

A butterfly graph is a type of network graph that resembles the shape of a butterfly when visualized. It is often used to represent parallel computations in computer science, particularly in the context of networks and interconnection systems. The butterfly graph has specific properties that make it useful for various applications, including: 1. **Structure**: A butterfly graph is typically defined recursively, meaning that it is constructed in layers.

A Golomb graph is a specific type of graph associated with the Golomb ruler, which is a set of markings at integer positions along an imaginary ruler such that no two pairs of markings have the same distance between them. In terms of graph theory, the Golomb graph is derived from the properties of such rulers. In a Golomb graph, each marking on the ruler corresponds to a vertex in the graph.

The Kittell graph, also known as the Kittell–Johnson graph, is a specific type of graph in graph theory. It is notable for its properties and structure, particularly in relation to its applications in combinatorial designs and algebraic constructions. Some of the key features of the Kittell graph include: - **Vertices and Edges:** The vertices of the graph represent certain combinatorial objects, and the edges depict specific relationships or interactions between these objects.

A tetrahedron is a type of polyhedron that has four triangular faces, six edges, and four vertices. It is one of the simplest three-dimensional shapes in geometry and is categorized as a type of simplex in higher-dimensional spaces. The most common example of a tetrahedron is a regular tetrahedron, where all the edges are of equal length and each face is an equilateral triangle. In regular tetrahedra, the vertices are equidistant from each other.

A truncated tetrahedron is a type of Archimedean solid that is formed by truncating (or cutting off) the corners (vertices) of a regular tetrahedron. This process involves slicing off each of the four vertices of the tetrahedron, resulting in a new solid with additional faces.

Grandi's series is an infinite series defined as follows: \[ S = 1 - 1 + 1 - 1 + 1 - 1 + \ldots \] It alternates between 1 and -1 indefinitely.

Operator algebras is a branch of functional analysis and mathematics that studies algebras of bounded linear operators on a Hilbert space. These algebras are typically closed in a specific topology (usually the operator norm topology or the weak operator topology), which makes them particularly amenable to the tools of functional analysis, topology, and representation theory.

Action selection is a fundamental process in decision-making systems, particularly in the fields of artificial intelligence (AI), robotics, and cognitive science. It refers to the method by which an agent or a system decides on a specific action from a set of possible actions in a given situation or environment. The goal of action selection is to choose the action that maximizes the agent's performance, achieves a particular goal, or yields the best outcome based on certain criteria.

The term "bipolar theorem" is often used in the context of convex analysis and mathematical optimization. Specifically, it relates to the relationships between sets and their convex cones.

A C*-algebra is a type of algebraic structure that arises in functional analysis and is fundamental to the study of operator theory and quantum mechanics.

The **closed graph property** is a concept from functional analysis that pertains to the relationship between the topology of a space and the continuity of operators between those spaces. In more precise terms, let \( X \) and \( Y \) be topological vector spaces, and let \( T: X \to Y \) be a linear operator.

In functional analysis and related fields of mathematics, a **complemented subspace** is a type of subspace of a vector space that has a certain structure with respect to the entire space. More specifically, consider a vector space \( V \) and a subspace \( W \subseteq V \).

High-dimensional statistics refers to the branch of statistics that deals with data that has a large number of dimensions (or variables) relative to the number of observations. In high-dimensional settings, the number of variables (p) can be much larger than the number of observations (n), leading to several challenges and phenomena that are distinct from traditional low-dimensional statistics.

Constructive quantum field theory (CQFT) is a branch of theoretical physics that aims to provide rigorous mathematical foundations to quantum field theory (QFT). Traditional approaches to QFT often involve perturbative techniques and heuristic arguments, which can sometimes lead to ambiguities or inconsistencies. In contrast, CQFT seeks to establish a solid mathematical framework for QFT by developing and rigorously proving results using techniques from advanced mathematics, such as operator algebras, functional analysis, and topology.

Convolution power is a concept used primarily in the field of probability theory and signal processing. It refers to the repeated application of the convolution operation to a probability distribution or a function. The convolution of two functions (or distributions) combines them into a new function that reflects the overlap of their values, effectively creating a new distribution that represents the sum of independent random variables, for example.

The term "functional square root" generally refers to a concept in mathematics where one function is considered the square root of another function. More formally, if \( f(x) \) is a function, then a function \( g(x) \) can be considered a functional square root of \( f(x) \) if: \[ g(x)^2 = f(x) \] for all \( x \) in the domain of interest.

A **Hadamard space** is a specific type of metric space that generalizes the concept of non-positive curvature. More formally, a Hadamard space is a complete metric space where any two points can be connected by a geodesic, and all triangles in the space are "thin" in a sense that closely resembles the behavior of triangles in hyperbolic geometry.