connected graph

connected graph

[kə′nek·təd ′graf]
(mathematics)
A graph in which each pair of points is connected by a path.

connected graph

(mathematics)
A graph such that there is a path between any pair of nodes (via zero or more other nodes).

Thus if we start from any node and visit all nodes connected to it by a single edge, then all nodes connected to any of them, and so on, then we will eventually have visited every node in the connected graph.
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We therefore adopt and extend the approach employed by Mike Keith to study the related problems of king-and queen-graphable words [2], Specifically, we define an alphabet A as a set of letters, and a word graph for a word with 1 [less than or equal to] n [less than or equal to] [absolute value of A] distinct letters as the connected graph of order n that has an edge (a<sub>1</sub>, a<sub>2</sub>) if the letters a<sub>1</sub>, a<sub>2</sub> [member of] A are adjacent to each other in the word, irrespective of order.
Let G be a connected graph with n vertices and m edges.
For a simple connected graph G the square of G is denoted by [G.
A CDS is a sub graph of a given undirected connected graph such that all nodes in the graph are included in the CDS or directly attached to a node (i.
In our method, extended Gaussian image [7] is first used to divide the 3D model surfaces and to obtain basic feature areas on the model, then the geodesic curves are generated to connect some selected feature areas, and finally a connected graph descriptor of local features is generated based on the geodesic path.
For every odd positive integer [alpha] > 3, find a connected graph G different from a tree, such that [alpha](G) = [alpha], and I(G;x) is palindromic and has only real roots.
Let G = (V,E) be a simple connected graph without self-loops and parallel edges where V={[v.
5 [7] For any non-complete connected graph G, (i)[gamma](G) [less than or equal to] [[gamma].
Since a connected graph on m nodes must have at least m -1 edges, the statement follows from Corollary 2.
It implements a sophisticated node-link drawing capability that allows custom screen objects to serve as parts of a connected graph.
In summary, a word W corresponds to some connected graph with n nodes and e edges, where e is the number of unique unordered bigrams in the word.
The Square of every two connected graph is Hamiltonian, J.
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