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1	Interpolating and dominating sequences Black, Ethan 13 May 2022 (has links) In this thesis we will be working with dominating and interpolating sequences. We worked with a geometric approach and used pseudohyperbolic translated to the Euclidean disc in order to show that a sequence within a certain radius of a dominating sequence is dominating as well. Interpolating sequences dominating sequences
2	Vertex Sequences in Graphs Haynes, Teresa W., Hedetniemi, Stephen T. 01 January 2021 (has links) 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. connected domination dominating sequences domination grid graphs irredundance total domination vertex cover vertex sequences zero forcing number Mathematics and Statistics