Sentence examples for path of order from inspiring English sources

For every positive integer n, we denote the path of order n, by (P_n).

The diameter of a connected graph G, denoted by (d(G)), is the maximum distance among all pairs of vertices in G. Let (S_{n}) and (P_{n}) be the star and the path of order n, respectively.

Let now v be a vertex with degree 2 in C 4 of P l 1, l 2. Then P l 1, l 2 − v = P n − 1, a path of order n − 1.

Denote by T l 1, l 2, l 3 the starlike tree with exactly one vertex v of degree 3, and T l 1, l 2, l 3 − v = P l 1 ∪ P l 2 ∪ P l 3, where P l i is the path of order l i ( i = 1, 2, 3 ).

This implies that d ( T ) = 5 and T ≅ S a, b 3 for some integers a, b with a + b = n − 4. If a = b = 1, then T is isomorphic to a path of order 6 and a straightforward calculation shows that S ( T ) = 5 + 3 < n + 1.5, as claimed.

This latter property stems from the fact that a system near its critical point is not very sensitive to the nature of the detailed properties of its components subsystems or to the details of the microscopic interactions, instead it depends on the more fundamental characteristics (i.e. symmetry, dimension, path of order propagation) of the system [11].

It has Hölder-continuous paths of order (delta< HK), and its paths are not differentiable.

In this paper, we want to complete the case m=4 by determining the set of all the integers v such that there is a path design of order v and block size 3 embedded in a 4-cycle system of order n.

In this paper, necessary and sufficient conditions are found for embedding a maximal partial 3-path design of order n into a 3-path design of specified order.

Also solved is the more general problem of finding necessary and sufficient conditions for the embedding of a partial 3-path design of order n into a 3-path design of order k≥n+2.

For example, in multi-path routing protocol such as Temporally-ordered routing algorithm (TORA) [28], OOO may occur if packets from different paths are out-of-order.