On tree-complete graphs
Ladislav Nebeský (1975)
Časopis pro pěstování matematiky
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Ladislav Nebeský (1975)
Časopis pro pěstování matematiky
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Gary Chartrand, Ortrud R. Oellermann, Song Lin Tian, Hung Bin Zou (1989)
Časopis pro pěstování matematiky
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Jason T. Hedetniemi (2015)
Discussiones Mathematicae Graph Theory
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Unique minimum vertex dominating sets in the Cartesian product of a graph with a complete graph are considered. We first give properties of such sets when they exist. We then show that when the first factor of the product is a tree, consideration of the tree alone is sufficient to determine if the product has a unique minimum dominating set.
Bohdan Zelinka (1994)
Mathematica Bohemica
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An extended tree of a graph is a certain analogue of spanning tree. It is defined by means of vertex splitting. The properties of these trees are studied, mainly for complete graphs.
Allan Bickle (2013)
Discussiones Mathematicae Graph Theory
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A set of vertices of a graph G is a total dominating set if each vertex of G is adjacent to a vertex in the set. The total domination number of a graph Υt (G) is the minimum size of a total dominating set. We provide a short proof of the result that Υt (G) ≤ 2/3n for connected graphs with n ≥ 3 and a short characterization of the extremal graphs.
Fatemeh Alinaghipour Taklimi, Shaun Fallat, Karen Meagher (2014)
Special Matrices
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The zero forcing number and the positive zero forcing number of a graph are two graph parameters that arise from two types of graph colourings. The zero forcing number is an upper bound on the minimum number of induced paths in the graph that cover all the vertices of the graph, while the positive zero forcing number is an upper bound on the minimum number of induced trees in the graph needed to cover all the vertices in the graph. We show that for a block-cycle graph the zero forcing...