Assertion: graph's vertex | /r/HasProperty | adjacent
Facets:
value: to the current vertex
type: LOCATION
value: in g
type: LOCATION
value: in h.
type: LOCATION
value: if
type: DEGREE
value: to v
type: LOCATION
value: in the graph
type: LOCATION
value: to it
type: OTHER
value: to one another
type: TRANSITIVE-OBJECT
value: to u
type: LOCATION
value: adjacent to v
type: OTHER
value: to the second
type: TEMPORAL
value: in h
type: LOCATION
value: v n-1
type: OTHER
value: to every vertex in x
type: LOCATION
value: similarly
type: MANNER
value: given a graph
type: OTHER
value: formally
type: DEGREE
Source sentences:
text: Two vertices, v and w, of a graph are ADJACENT if there is an edge, vx, joining theem; the vertices are then considered INCIDENT to the edge, vx.
text: A u-v walk is defined as a sequence of vertices starting at u and ending at v , where consecutive vertices in the sequence are adjacent vertices in the graph
text: Formally, given a graph G = (V, E), two vertices v i , v j Î V are said to be neighbors, or adjacent nodes, if ( v i
text: Similarly, two vertices are called adjacent if they share a common edge (consecutive if the first one is the tail and the second one is the head of an edge), in which case the common edge is said to join the two vertices.
text: In a complete bipartite graph, the vertex set is the union of two disjoint sets, W and X, so that every vertex in W is adjacent to every vertex in X but there are no edges within W or X.
text: G is a graph the vertices of which correspond to the edges of G, any two vertices of H being adjacent if and…
text: first order The first order logic of graphs is a form of logic in which variables represent vertices of a graph, and there exists a binary predicate to test whether two vertices are adjacent.
text: v is the subgraph induced by all vertices that are adjacent to v .
text: The inverse operation to a graph power: a k th root of a graph G is another graph on the same vertex set such that two vertices are adjacent in G if and only if they have distance at most k in the root.
text: Then, two vertices of T are adjacent if one is a simple extension of another: the vertex (r, v 1 , v 2 , ..., v n ) is adjacent to the vertex (r, v 1 , v 2 , ..., v n-1 ).
text: Then, two vertices of T are adjacent if one is a simple extension of another: the vertex (r, v 1 , v 2 , ..., v n ) is adjacent to the vertex (r, v 1 , v 2 , ..., v n-1 ).
text: In the mathematical area of graph theory, a clique ( or ) is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are adjacent; that is, its induced subgraph is complete.
text: A clique, C, in an undirected graph G = (V, E) is a subset of the vertices, C ⊆ V, such that every two distinct vertices are adjacent.
text: A vertex w is said to be adjacent to another vertex v if the graph contains an edge (v,w).
text: A universal vertex is a vertex that is adjacent to every other vertex in the graph.
text: Essentially, it represents which vertices are adjacent, or rather, which pairs of vertices have an edge.
text: A t-arc is defined to be a sequence of t+1 vertices, such that any two consecutive vertices in the sequence are adjacent, and with any repeated vertices being more than 2 steps apart.
text: Alternatively, by the circle packing theorem, any planar graph may be represented as a collection of circles, any two of which cross if and only if the corresponding vertices are adjacent; these circles (with a starting and ending point chosen to turn them into open curves) provide a string graph representation of the given planar graph.
text: In graph theory, the complement or inverse of a graph G is a graph H on the same vertices such that two distinct vertices of H are adjacent if and only if they are not adjacent in G.
text: such that any two vertices u and v of G are adjacent in G if and only if f(u) and f(v) are adjacent in H.
text: such that any two vertices u and v of G are adjacent in G if and only if f(u) and f(v) are adjacent in H.
text: An alternative and equivalent definition of a graph minor is that H is a minor of G whenever the vertices of H can be represented by a collection of vertex-disjoint subtrees of G, such that if two vertices are adjacent in H, there exists an edge with its endpoints in the corresponding two trees in G.
text: In the same way that an intersection representation of a graph labels every vertex with a set so that vertices are adjacent if and only if their sets have nonempty intersection, so an inclusion representation f of a poset labels every element with a set so that for any x and y in the poset, x
text: An initial or source vertex is identified to start traversing, then from that vertex any one vertex which is adjacent to the current vertex is traversed
text: In other words it can be stated as all vertices that are adjacent to the current vertex are traversed first.
text: The first vertex is said to be adjacent to the second.
text: To determine if two vertices are adjacent, search the edge set for an edge having the first vertex as its from field, and the second vertex as its to field.
text: Given a graph G {\displaystyle G} , and another graph G ′ {\displaystyle G'} , G ′ {\displaystyle G'} is called an I G {\displaystyle IG} if G ′ {\displaystyle G'} is formed from G {\displaystyle G} by replacing the vertices of G {\displaystyle G} with connected graphs such that if a vertex v {\displaystyle v} is replaced by a connected graph G v {\displaystyle G_{v}} , there are edges connecting G v {\displaystyle G_{v}} to each of the graphs replacing the vertices that are adjacent to v {\displaystyle v} in G {\displaystyle G} , and only to those graphs.
text: This means that any other vertex can be either adjacent to u {\displaystyle u} or adjacent to v {\displaystyle v} .
text: such that any two vertices u and v of G are adjacent in G if and only if ƒ(u) and ƒ(v) are adjacent in H.
text: such that any two vertices u and v of G are adjacent in G if and only if ƒ(u) and ƒ(v) are adjacent in H.
text: The complement or inverse of a graph G is a graph H on the same vertices such that two vertices of H are adjacent if and only if they are not adjacent in G.
text: When an edge connects two vertices, we say that the vertices are adjacent to one another and that the edge is incident on both vertices.
text: Visit (recursively) all the vertices that are adjacent to it
text: is defined as a sequence of vertices starting at and ending at , where consecutive vertices in the sequence are adjacent vertices in the graph