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The Global ETD Search service is a free service for researchers
to find electronic theses and dissertations. This service is
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Networked Digital Library of Theses and Dissertations.
Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
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Showing 1 to 6 of 6 (0.118 seconds)| 1 |
Connected Domination Stable Graphs Upon Edge AdditionDesormeaux, Wyatt J., Haynes, Teresa W., van der Merwe, Lucas 04 December 2015 (has links)
A set S of vertices in a graph G is a connected dominating set of G if S dominates G and the subgraph induced by S is connected. We study the graphs for which adding any edge does not change the connected domination number.
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Bounds on the Connected Domination Number of a GraphDesormeaux, Wyatt J., Haynes, Teresa W., Henning, Michael A. 01 December 2013 (has links)
A subset S of vertices in a graph G=(V,E) is a connected dominating set of G if every vertex of V\-S is adjacent to a vertex in S and the subgraph induced by S is connected. The minimum cardinality of a connected dominating set of G is the connected domination number γc(G). The girth g(G) is the length of a shortest cycle in G. We show that if G is a connected graph that contains at least one cycle, then γc(G)≥g(G)-2, and we characterize the graphs obtaining equality in this bound. We also establish various upper bounds on the connected domination number of a graph, as well as Nordhaus-Gaddum type results.
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Bounds on the Connected Domination Number of a GraphDesormeaux, Wyatt J., Haynes, Teresa W., Henning, Michael A. 01 December 2013 (has links)
A subset S of vertices in a graph G=(V,E) is a connected dominating set of G if every vertex of V\-S is adjacent to a vertex in S and the subgraph induced by S is connected. The minimum cardinality of a connected dominating set of G is the connected domination number γc(G). The girth g(G) is the length of a shortest cycle in G. We show that if G is a connected graph that contains at least one cycle, then γc(G)≥g(G)-2, and we characterize the graphs obtaining equality in this bound. We also establish various upper bounds on the connected domination number of a graph, as well as Nordhaus-Gaddum type results.
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Bounds on the Global Domination NumberDesormeaux, Wyatt J., Gibson, Philip E., Haynes, Teresa W. 01 January 2015 (has links)
A set S of vertices in a graph G is a global dominating set of G if S simultaneously dominates both G and its complement Ḡ. The minimum cardinality of a global dominating set of G is the global domination number of G. We determine bounds on the global domination number of a graph and relationships between it and other domination related parameters.
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Domination Parameters of a Graph and Its ComplementDesormeaux, Wyatt J., Haynes, Teresa W., Henning, Michael A. 01 January 2018 (has links)
A dominating set in a graph G is a set S of vertices such that every vertex in V (G) \ S is adjacent to at least one vertex in S, and the domination number of G is the minimum cardinality of a dominating set of G. Placing constraints on a dominating set yields different domination parameters, including total, connected, restrained, and clique domination numbers. In this paper, we study relationships among domination parameters of a graph and its complement.
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Vertex Sequences in GraphsHaynes, 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.
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