Give definitions of the following terms: 1) Graph ii) Tree iii) Weighted Graph iv) Cycle v) Spanning Tree
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Answer:
In the mathematical field of graph theory, a spanning tree T of an undirected graph G is a subgraph that is a tree which includes all of the vertices of G. In general, a graph may have several spanning trees, but a graph that is not connected will not contain a spanning tree (see spanning forests below). If all of the edges of G are also edges of a spanning tree T of G, then G is a tree and is identical to T (that is, a tree has a unique spanning tree and it is itself).
Explanation:
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Answer:
1st : Graph : a diagram in which a line or a curve shows the relationship between two quantities, measurements, etc.
2nd : Tree : a tall plant that can live for a long time. Trees have a thick wooden central part from which branches grow
3rd : Weighted Graph : graph having a weight, or number, associated with each edge. Some algorithms require all weights to be nonnegative, integral, positive, etc. Also known as edge-weighted graph.
4th : Cycle : an interval of time during which a sequence of a recurring succession of events or phenomena is completed a 4-year cycle of growth and development.
5th : Spanning tree : A minimum spanning tree is a special kind of tree that minimizes the lengths (or “weights”) of the edges of the tree. An example is a cable company wanting to lay line to multiple neighborhoods; by minimizing the amount of cable laid, the cable company will save money. A tree has one path joins any two vertices.
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