Document Type
Review
Publication Date
1-1-2021
Description
We consider a variety of types of vertex sequences, which are defined in terms of a requirement that the next vertex in the sequence must meet. For example, let S = (v1, v2, …, vk ) be a sequence of distinct vertices in a graph G such that every vertex vi in S dominates at least one vertex in V that is not dominated by any of the vertices preceding it in the sequence S. Such a sequence of maximal length is called a dominating sequence since the set {v1, v2, …, vk } must be a dominating set of G. In this paper we survey the literature on dominating and other related sequences, and propose for future study several new types of vertex sequences, which suggest the beginning of a theory of vertex sequences in graphs.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Citation Information
Haynes, Teresa W.; and Hedetniemi, Stephen T.. 2021. Vertex Sequences in Graphs. Discrete Mathematics Letters. Vol.6 19-31. https://doi.org/10.47443/dml.2021.s103
Copyright Statement
c 2021 the authors. This is an open access article under the CC BY (International 4.0) license (www.creativecommons.org/licenses/by/4.0/).