G (A, B) - Labeling of forests and trees
Issue Date
2-2016
Abstract
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.
Source or Periodical Title
AIP Conference Proceedings
ISSN
0094-243X
Volume
1707
Page
020005-1 - 020005-9
Document Type
Conference Paper
Physical Description
illustrations
Language
English
Subject
algebraic graph constructions, graph theory, vertex labeling
Recommended Citation
Egarguin, N.J., Panopio, R.G. (2016). G(A, B) – labeling of forests and trees. AIP Conference Proceedings, 1707, 020005-1 - 020005-9. DOI:10.1063/1.4940806.
Identifier
DOI:10.1063/1.4940806.
Digital Copy
yes