In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group, [1] is a graph that encodes the abstract structure of a group. Its …

Mar 28, 2025 · The Cayley graph associated with (G,S) is then defined as the directed graph having one vertex associated with each group element and directed edges (g,h) whenever …

Cayley graphs give a way of encoding information about group in a graph. Given a group with a, typically nite, generating set, we can form a Cayley Graph for that group with respect to that …

Mar 29, 2024 · Cayley graphs provide graphic representations for abstract groups. They are a bridge between groups and surfaces, and they give rise to examples for various extremal …

Mar 12, 2025 · In geometric group theory, the Cayley graph (also: Cayley quiver) of a group, G G, equipped with a set of generators, X X, encodes how the chosen generating elements operate …

We will now examine two exciting types of Cayley graphs: Paley graphs and generalized hypercubes. The Paley graph are Cayley graphs over the group of integer modulo a prime, p, …

A Cayley graph is a special type of graph that represents the structure of a group, a fundamental concept in abstract algebra. It is constructed using a set of generators, which are a subset of …

So far, we've seen three different kinds of groups: Groups of symmetries (including the dihedral group of symmetries of a polygon), the integers modulo \(n\), and the permutation group, …

The Cayley graph of Hgenerated by S, denoted Cay(H;S), is the directed graph G= (V;E) where V = Hand E= f(x;xs) jx2H;s2Sg. If S= S 1 (i.e., Sis closed under inverse), then Cay(H;S) is an …

In this paper, I will outline the basics of graph theory in an attempt to explore Cayley’s Formula. Cayley’s Formula is one of the most simple and elegant results in graph theory, and as a …