Assertion: graph's g | /r/HasProperty | connected
Facets:
value: for all s ⊆ v
type: OTHER
value: for <
type: PURPOSE
value: by removing just one vertex
type: MANNER
Source sentences:
text: G is connected, but would become disconnected if any single edge is removed from G .
text: such that G is k-connected, and is denoted by κ ( G )
text: , G is i-connected.
text: The above G can be disconnected by removing just one vertex i.e., vertex c .
text: If G is a connected graph, the spanning tree in G is a subgraph of G which includes every vertex of G and is also a tree.
text: Theorem: Let G be a k-connected graph.
text: A graph G is called k-connected if for every S ⊆ V ( G ) {\displaystyle S\subseteq V(G)} , and | S | <
text: (That is, G is connected and 1-degenerate.)
text: A graph G is connected if there is a path in G between any given pair of vertices, otherwise it is disconnected.
text: If there is a u-v path for every pair of vertices u and v in G, then we say that G is connected
text: If there are distinct vertices u and v in G so that G-u and G-v are both connected, then G is also connected.
text: Proof: Since G is k-connected, for all S ⊆ V ( G ) ,