Keywords: vertex-colored graph,

connected subgraph, tropical subgraph, colorful subgraph, vertex-colored random graph.

Network motif, as another concept describing local properties of a network, is defined as a small

connected subgraph that appears frequently and uniquely in a network.

We call R a trunk of F if R is a maximal

connected subgraph of F such that every colored vertex in R is a leaf of R.

R] (I(G)) is a integrity domain if and only if every

connected subgraph of G has either at most a cycle of odd length or no cycle of even length.

More formally, a graph is a knight subgraph if it is an isomorphism of some

connected subgraph of the infinite knight's graph.

A tree in G is a

connected subgraph T = (V', E') containing no cycles.

A dominating set is connected if it induces a

connected subgraph.

A cycle C in a graph is a

connected subgraph in which the degree of every vertex in C is two.

The task is to construct an undirected graph G in which every word in the lexical matrix covers a

connected subgraph and in which, furthermore, G does not contain a subgraph G' in which this is also the case.

A spanning tree of a

connected subgraph induced by S [union] T in G is called a Steiner tree.

The benefit of such shortcuts is that by avoiding one-child parents, we ensure that each of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] now has at least one vertex, which itself is a vertex of G or a contraction of a

connected subgraph.

A SQL subgraph is a

connected subgraph of a query graph consisting of SQL tables that belong to the same SQL database.