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Strongly regular graphs are a special class of graphs characterized by their regularity and specific connection properties between vertices. A graph \( G \) is called strongly regular with parameters \( (n, k, \lambda, \mu) \) if it satisfies the following conditions: 1. **Regularity**: The graph has \( n \) vertices, and each vertex has degree \( k \) (i.e., it is \( k \)-regular).

The Iofinova–Ivanov graph is a type of vertex-transitive graph that is defined using a specific set of rules based on combinatorial properties. The 110-vertex version of this graph specifically contains 110 vertices and has edges defined through particular mathematical relationships.

The Andrásfai graph is a specific type of graph in graph theory, distinguished for its properties related to being a strongly regular graph. It is named after the Hungarian mathematician János Andrásfai, who studied these structures. ### Properties of the Andrásfai Graph: 1. **Vertices and Edges**: The Andrásfai graph contains 18 vertices and 27 edges.

An antiprism graph is a geometric representation of a three-dimensional shape known as an antiprism. An antiprism is a polyhedron characterized by having two parallel polygonal bases connected by a band of triangular faces. The most common type of antiprism is the regular antiprism, where the bases are congruent regular polygons and the triangular faces are also isosceles triangles. In graph theory, the antiprism graph can be represented as a bipartite graph.

An Archimedean graph is a type of mathematical structure that is related to the concept of Archimedean solids in geometry. Specifically, an Archimedean graph is a vertex-transitive graph that can be represented as a Cayley graph of a group related to an Archimedean solid. In the context of geometry and polyhedra, Archimedean solids are convex polyhedra that are made up of two or more types of regular polygons.

The Balaban 10-cage is a specific type of polyhedron that is notable in the study of geometric structures and graph theory. It is a 3-dimensional shape that can be categorized as a type of cage, which is a regular polyhedron that has certain properties related to its vertices, edges, and faces.

The Balaban 11-cage is a type of graph that is part of a family of structures known as cage graphs. Cages are defined as regular graphs that have the smallest possible number of edges for a given number of vertices and girth (the length of the shortest cycle in the graph). Specifically, the Balaban 11-cage is an (11, 3)-cage, meaning it has 11 vertices and a girth of 3.

The Barnette–Bosák–Lederberg graph is an interesting example of a specific type of graph in the field of graph theory. It is notably a 3-connected cubic graph, meaning that it is a graph where each vertex has degree 3 (cubic) and it cannot be disconnected by removing just two vertices (3-connected). This graph is particularly recognized for having properties that make it an important object of study in relation to Hamiltonian paths and cycles.

The Bidiakis cube, also known as the Bidiakis knot, is a mathematical construct and a type of geometric puzzle. It is a variation of a cube that is often used in the study of topology and knot theory. The Bidiakis cube can also refer to a specific configuration of a geometric object where the cube exhibits certain twisting or knot-like properties, making it a subject of interest in mathematical visualization and education.

The Biggs–Smith graph is a specific type of graph in graph theory. It is defined as a 2-regular graph with 12 vertices and 12 edges. A 2-regular graph means that each vertex has a degree of 2, which implies that the graph consists of disjoint cycles.

Blanuša snarks are a specific type of snark, which is a type of non-trivial, 3-regular (each vertex has degree 3), edge-colored graph that lacks any homomorphic mapping to a 3-colorable graph, thus making it non-colorable with three colors. These graphs are named after the Croatian mathematician Josip Blanuša, who discovered them.

The Brinkmann graph is a specific type of graph in graph theory known for its unique properties. It is characterized as a 3-regular (cubic) graph, meaning that each vertex has exactly three edges connected to it.

In graph theory, a **cage** is a special type of graph that is defined by certain properties related to its vertices and edges. Specifically, a cage is a regular graph (a graph where each vertex has the same degree) with the fewest number of edges for a given degree and a specified girth (the length of the shortest cycle in the graph).

A Cameron graph is a specific type of graph that arises in combinatorics, particularly in the context of certain problems in graph theory and design theory. However, the term "Cameron graph" is not widely recognized in mathematical literature as a standard concept. It is possible that it refers to a specific graph or class of graphs studied by mathematicians like R. C. Cameron, who has made contributions to combinatorial designs and related areas.

Chang graphs, also known as Chang's graph or Chang's construction, are specific types of graphs in the field of combinatorial mathematics, particularly in graph theory. They are named after the mathematician Cheng-Chung Chang who introduced them in the context of studying properties of graphs and their applications in various areas of mathematics and computer science.

The Chvátal graph is a specific type of graph in the field of graph theory. It is a simple, undirected graph that consists of 12 vertices and 30 edges. The Chvátal graph is notable for several properties: 1. **Hamiltonian**: The Chvátal graph has a Hamiltonian cycle, meaning there exists a cycle that visits every vertex exactly once and returns to the starting vertex.

A **circulant graph** is a specific type of graph that generalizes the concept of cyclic graphs. It is defined using a description based on its vertex set and a set of connections (edges) determined by a set of step sizes.

Circular coloring is a concept in graph theory, specifically in the area of graph coloring. Unlike traditional graph coloring, where vertices of a graph are colored such that no two adjacent vertices share the same color, circular coloring allows for a more flexible coloring scheme: instead of using discrete colors, it uses a continuous spectrum of colors represented on a circle. In circular coloring, each vertex is assigned a position on the circumference of a circle, which corresponds to a color on a continuous scale.

The Clebsch graph is a specific type of graph in graph theory, notable for its unique mathematical properties. It has 16 vertices and 40 edges. The Clebsch graph can be described as a regular graph, meaning that each vertex has the same degree; specifically, each vertex in the Clebsch graph has a degree of 5.

A **complete graph** is a type of graph in which every pair of distinct vertices is connected by a unique edge. Complete graphs are denoted by the symbol \( K_n \), where \( n \) represents the number of vertices in the graph.