Sentence examples for exists a connected from inspiring English sources

We say that two vertices are weakly connected if there exists a connected path between two vertices when all directed edges are replaced with undirected edges.

Then for any j ∈ ℕ, there exists a connected component C j of the set of nontrivial solutions for (P) connecting (0, λ j (p)) to (∞, λ j (q)) such that ( u, λ ) ∈ C j implies that u has exactly j - 1 simple zeros in (0, 1), where λ j (r) is the j-th eigenvalue of (ϕ r (u'(t)))' + λϕ r (u(t)) = 0 and u(0) = u(1) = 0.

Then there exists a connected branch of such that (1.7).

So there exists a connected component of solutions of (2.30) containing, and either.

By Lemma 1.2, there exists a connected branch of such that for any.

We are to prove that for any positive integer, there exists a connected branch of satisfying (4.9).

A clique is a subset of nodes such that for every two nodes in, there exists an link connecting the two.

A clique is a subset of nodes such that for every two nodes in clique, there exists an link connecting the two.

Moreover, there exists a termwise connected sequence ({x_{n}}) in X such that (x_{n+k}in T(x_{n},x_{n+1},ldots,x_{n+k-1})) for all (ninmathbb{N}) and ({x_{n}} ) converges to a fixed point of T. There exists a path ({x_{i}}_{i=1}^{k+1}) of (k+1) vertices in G such that (x_{k+1}in T(x_{1},ldots,x_{k},x_{k})).

We assume here a connected graph, that is, there exists a path connecting any pair of distinct nodes.

We assume here a connected graph; that is, there exists a path connecting any pair of distinct nodes in the network.