| Popis: |
Let G be a group or a ring with non-empty subsets A and B. The graph G(A, B) is the simple graph obtained by deleting all loops from the graph with vertex set A and where vertices x and y are adjacent if and only if there is a b ∈ B such that xb = y or yb = x. It can also be defined using a group G acting on a set X by replacing A by a subset of X and vertices x and y are adjacent if and only if there is a b ∈ B ⊆ G such that (b, x) ↦ y or (b, y) ↦ x.In this paper, we shall present several structural properties of G(A, B)’s leading to establishing ways of realizing forests and trees as labeled graphs over groups and rings. |
