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.
| Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etsu-works-11118 |
| Date | 01 January 2021 |
| Creators | Haynes, Teresa W., Hedetniemi, Stephen T. |
| Publisher | Digital Commons @ East Tennessee State University |
| Source Sets | East Tennessee State University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | ETSU Faculty Works |
| Rights | http://creativecommons.org/licenses/by/4.0/ |
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