Sentence examples for connectivity exactly from inspiring English sources

In this section, we consider the degree sequence of multi-digraphs with connectivity exactly k.

Assume d is the degree sequence of some multi-digraph D with connectivity exactly k.

Then d is a degree sequence of some multi-digraph with connectivity exactly k if and only if each of the following hold.

In this paper, we will use these operations to obtain a k-arc-connected digraph or a digraph with arc-connectivity exactly k from an arbitrary digraph in (langlemathbf {d}rangle).

In this paper, characterizations for k-arc-connected realizable sequences and realizable sequences with arc-connectivity exactly k are given.

Furthermore, we also give a characterization for multi-digraphs with arc-connectivity exactly k.

Also, when (ngeq6), we give a sufficient and necessary condition of d to have a realization D that has arc-connectivity exactly k.

Furthermore, if Theorem 4.1 iii) does not hold, then there are no digraphs in (langlecdotrangle) that have arc-connectivity exactly k.

In Section 4, we characterize the sequence of pairs of integers to have a realization that has arc-connectivity exactly k.

If (D_{m}) has arc-connectivity at most k, then by Claim 3 there exists i such that (D_{i}) has arc-connectivity exactly k, and we are done.

So we may assume that (lambda(D >k), then we will construct a multi-digraph in (langlemathbf {d}rangle) with arc-connectivity exactly k from D. First, we need some claims.