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In 2015, it was announced that Harman International Industries were interested in acquiring Symphony Teleca. [11] Harman and Symphony Technology Group agreed on a deal worth US$780 million. [12] Teleca was rebranded Harman Connected Services, with a focus on producing software for all Harman-related products. [13] As well as Symphony Teleca, Harman also acquired Red Bend Software. The total ...
In graph theory, a biconnected graph is a connected and "nonseparable" graph, meaning that if any one vertex were to be removed, the graph will remain connected. Therefore a biconnected graph has no articulation vertices. The property of being 2-connected is equivalent to biconnectivity, except that the complete graph of two vertices is usually not regarded as 2-connected. This property is ...
Proposition— For a topological space , the following conditions are equivalent: X {\displaystyle X} is connected, that is, it cannot be divided into two disjoint non-empty open sets. The only subsets of X {\displaystyle X} which are both open and closed (clopen sets) are X {\displaystyle X} and the empty set. The only subsets of X {\displaystyle X} with empty boundary are X {\displaystyle X ...
One of the most important facts about connectivity in graphs is Menger's theorem, which characterizes the connectivity and edge-connectivity of a graph in terms of the number of independent paths between vertices. If u and v are vertices of a graph G, then a collection of paths between u and v is called independent if no two of them share a vertex (other than u and v themselves). Similarly ...
A simple alternative to the above algorithm uses chain decompositions, which are special ear decompositions depending on DFS -trees. [3] Chain decompositions can be computed in linear time by this traversing rule. Let C be a chain decomposition of G. Then G is 2-vertex-connected if and only if G has minimum degree 2 and C1 is the only cycle in C. This gives immediately a linear-time 2 ...
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Let be a homogeneous relation. The following are equivalent: [14] is strongly connected; ; ; is asymmetric, where is the universal relation and is the converse relation of The following are equivalent: [14] R {\displaystyle R} is connected; I ¯ ⊆ R ∪ R ⊤ {\displaystyle {\overline {I}}\subseteq R\cup R^ {\top }} ; R ¯ ⊆ R ⊤ ∪ I {\displaystyle {\overline {R}}\subseteq R^ {\top ...