Reducing the adjacency matrix of a tree.
Fricke, Gerd H.; Hedetniemi, Stephen T.; Jacobs, David P.; Trevisan, Vilmar — 1996
ELA. The Electronic Journal of Linear Algebra [electronic only]
Reducing the adjacency matrix of a tree.
Domination Subdivision Numbers
A set S of vertices of a graph G = (V,E) is a dominating set if every vertex of V-S is adjacent to some vertex in S. The domination number γ(G) is the minimum cardinality of a dominating set of G, and the domination subdivision number is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the domination number. Arumugam conjectured that for any graph G. We give a counterexample to this conjecture. On the other hand, we show...
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