Sentence examples for degrees tree from inspiring English sources

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Example 2 A uniformly bounded degree tree satisfies assumption (5).

We call T a controlled tree if it is a non-uniformly bounded-degree tree when the assumption (5) holds.

If the degrees of all vertices on a tree T are uniformly bounded, then we call T a uniformly bounded degree tree (see [1] and [2]).

In this section, we mainly consider a controlled tree, which is a non-uniformly bounded-degree tree with assumption (5) holding.

If we consider any uniformly bounded-degree tree, then there are some (a>0) such that (d^{N}_{n}leq a^{N}), (|{tin T^{(n)}: d^{N}(t)> a^{N} }|=0), which indicates that uniformly bounded-degree trees conform to the assumption (5).

As information needs to be spread in only one direction (from gateway) through a low-degree tree, and since only nodes that need to activate some inactive nodes (on the periphery of the current topology) would be scheduled for transmission in these slots, the TDMA configuration frame of 8 slots is enough for collision-free transmission scheduling of a degree-4 tree with 2-hop coloring.

In fact, if the tree T is a uniformly bounded degree tree, then max { d N ( t ) : t ∈ T ( n − N ) } is no more than a constant a N, and ln | T ( n ) | | T ( n − N ) | ≤ ln | T ( n − N ) | × a N | T ( n − N ) | = N ln a. is also a constant.

It is proven in this paper that the considered problem is strongly NP-complete even for node-weighted trees (the weight of each edge is 1) with one vertex of degree greater than 2. It is also shown that there exists a polynomial-time algorithm for finding an optimal connected search strategy for a given bounded degree tree with arbitrary weights on the edges and on the vertices.

The outcomes generalize some known results on regular trees and uniformly bounded degree trees.

Huang and Yang [2] studied the strong law of large numbers for Markov chains indexed by uniformly bounded degree trees.