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If it is possible to establish a path from any vertex to any other vertex of a graph, the graph is said to be connected. |
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A connected graph without cycles is said a tree; equivalently, a tree on n vertices is a connected graph with exactly n-1 edges. Trees are largely used as data structures in computer science (see tree data structure). |
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A complete graph is one in which every node is adjacent to every other node. The above graph is not complete. The complete graph on n vertices is often denoted by Kn. |
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A complete graph is one in which every node is adjacent to every other node. The above graph is not complete. The complete graph on n vertices is often denoted by Kn. It has n(n-1)/2 edges (corresponding to all possible choices of pairs of vertices). |
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