A distance-regular graph is a specific type of graph that has a high degree of regularity in the distances between pairs of vertices. Formally, a graph \( G \) is said to be distance-regular if it satisfies the following conditions: 1. **Regularity**: The graph is \( k \)-regular, meaning each vertex has exactly \( k \) neighbors.

Maude is a high-level programming language and system that is based on rewriting logic. It is designed for specifying, programming, and reasoning about systems in a formal and executable manner. Maude allows for the definition of systems in terms of algebraic specifications, and it can be used for a wide range of applications in formal methods, including model checking, theorem proving, and symbolic simulation.

Graph automorphism is a concept in graph theory that refers to a symmetry of a graph that preserves its structure. More specifically, an automorphism of a graph is a bijection (one-to-one and onto mapping) from the set of vertices of the graph to itself that preserves the adjacency relationship between vertices.

The Ihara zeta function is a mathematical object that arises in the study of finite graphs, particularly in the context of algebraic topology and number theory. It was introduced by Yoshio Ihara in the 1960s.

Mac Lane's planarity criterion, also known as the "Mac Lane's formation", is a combinatorial condition used to determine whether a graph can be embedded in the plane without any edges crossing. Specifically, the criterion states that a graph is planar if and only if it does not contain a specific type of subgraph as a "minor.

The Parry–Sullivan invariant is a concept in the field of dynamical systems and statistical mechanics, particularly related to the study of interval exchanges and translations. It is associated with the study of the dynamics of certain classes of transformations, particularly those that exhibit specific structural and statistical properties. The invariant itself is often connected to topological and measure-theoretic characteristics of systems that exhibit a certain type of symmetry or recurrence.

Sims' conjecture is a hypothesis in the field of algebraic topology and combinatorial group theory, specifically relating to the properties of certain types of groups. Named after mathematician Charles Sims, the conjecture primarily deals with the structure of finite groups and representation theory. While specific details or formulations may vary, Sims' conjecture is generally focused on establishing a relationship between the orders of groups and their representations or modules.

A strongly regular graph is a specific type of graph characterized by a regular structure that satisfies certain conditions regarding its vertices and edges. Formally, a strongly regular graph \( G \) is defined by three parameters \( (n, k, \lambda, \mu) \) where: - \( n \) is the total number of vertices in the graph.

A **vertex-transitive graph** is a type of graph in which, for any two vertices, there is some automorphism of the graph that maps one vertex to the other. In simpler terms, this means that the graph looks the same from the perspective of any vertex; all vertices have a similar structural role within the graph. ### Key Properties: 1. **Automorphism:** An automorphism is a bijection (one-to-one correspondence) from the graph to itself that preserves the edges.

Barbara L. Osofsky is a prominent figure in the field of law, particularly known for her contributions to the field of legal education and health law. She has been recognized for her work in various legal areas, including her advocacy for legal issues related to health and medicine. Her writings and research often focus on the intersection of law, ethics, and public health. If you were looking for specific information or a different context regarding Barbara L. Osofsky, please provide more details!

Bjarni Jónsson is a name that can refer to different individuals, but without additional context, it is difficult to determine exactly who you're referring to. If you're asking about a notable person, it could be an Icelandic figure, as Bjarni Jónsson is a common name in Iceland. There may be athletes, academics, or artists by that name.

Chiungtze C. Tsen is a notable figure in the fields of mathematics and education, particularly known for her contributions to mathematical research and her role in academia. She has published research in various mathematical topics and has been involved in educational initiatives aimed at improving mathematics education.

D. S. Malik is an author known for his contributions to the field of computer science and programming. He is particularly recognized for his textbooks related to programming languages, data structures, and algorithms. One of his notable works is "Data Structures Using C," which is widely used in academic settings to teach data structures through the C programming language.

Dave Bayer is an American mathematician known for his work in various areas of mathematics, including algebra and combinatorics. He is also recognized for his contributions to mathematical education and outreach. Bayer has published numerous papers and is involved in promoting mathematical understanding through teaching and public engagement.

David Eisenbud is a prominent American mathematician known for his work in algebraic geometry, commutative algebra, and related fields. He has made significant contributions to the study of singularities, mixed characteristic, and the interplay between algebra and geometry. Eisenbud has also been involved in various educational efforts and served in administrative roles, including as the director of the Mathematical Sciences Research Institute (MSRI) in Berkeley, California.

Donald S. Passman is an American entertainment attorney known for his expertise in the music industry. He has represented a variety of high-profile artists, songwriters, and music publishers. Passman is well-known for his book "All You Need to Know About the Music Business," which provides insights into the complexities of the music industry, including contracts, rights, and the various roles within the music business.

As of my last update in October 2023, there is no widely known figure by the name Ellen Kirkman in popular culture, history, or current events. It's possible that she could be a private individual or a subject relevant to a niche area not widely recognized.

An **acylindrically hyperbolic group** is a type of group in geometric group theory that generalizes the concept of hyperbolic groups. These groups are characterized by a specific type of action they have on a $\textit{proper geodesic metric space}$.

Ann Cartwright is a name that could refer to several individuals, but in a prominent context, she is known as a philosopher of science, particularly recognized for her work on the philosophy of physics and the foundations of scientific theories. She has contributed significantly to discussions surrounding the nature of scientific explanations, causal relationships, and the interpretation of scientific theories.