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Full-Text Articles in Physical Sciences and Mathematics
Bounds For The Independence Number Of A Graph, William Willis
Bounds For The Independence Number Of A Graph, William Willis
Theses and Dissertations
The independence number of a graph is the maximum number of vertices from the vertex set of the graph such that no two vertices are adjacent. We systematically examine a collection of upper bounds for the independence number to determine graphs for which each upper bound is better than any other upper bound considered. A similar investigation follows for lower bounds. In several instances a graph cannot be found. We also include graphs for which no bound equals $\alpha$ and bounds which do not apply to general graphs.
Parity Domination In Product Graphs, Christopher Whisenant
Parity Domination In Product Graphs, Christopher Whisenant
Theses and Dissertations
An odd open dominating set of a graph is a subset of the graph’s vertices with the property that the open neighborhood of each vertex in the graph contains an odd number of vertices in the subset. An odd closed r-dominating set is a subset of the graph’s vertices with the property that the closed r-ball centered at each vertex in the graph contains an odd number of vertices in the subset. We first prove that the n-fold direct product of simple graphs has an odd open dominating set if and only if each factor has an odd open dominating …
Embeddings Of Product Graphs Where One Factor Is A Hypercube, Bethany Turner
Embeddings Of Product Graphs Where One Factor Is A Hypercube, Bethany Turner
Theses and Dissertations
Voltage graph theory can be used to describe embeddings of product graphs if one factor is a Cayley graph. We use voltage graphs to explore embeddings of various products where one factor is a hypercube, describing some minimal and symmetrical embeddings. We then define a graph product, the weak symmetric difference, and illustrate a voltage graph construction useful for obtaining an embedding of the weak symmetric difference of an arbitrary graph with a hypercube.