Graph unconnected

An unconnected graph is a graph in which not all its nodes can be connected by a certain sequence of arcs. 

A directed forest is a term for the unconnected directed graph in which every component of connection is a directed tree with a root. ... 

If one attempts to understand the expansion factor as an inner parameter, taking the expansion matrix as an operator acting differential equation can be solved only in the case of totally unstructured and unconnected graphs. 

Any complete bipartite graph fCm,n9 is a join of two completely unconnected (edgeless) graphs (mi = 0, m2 = 0). 

The permutation groups of degree n used hereafter are g ven in Table 5. The symmetric group Sn is the automorphism group of the complete graph, /Cn, us well as that of its complement, the completdy unconnected graph having n isolated vertices. 

Complete bipartite graphs can be thought of as a join of two completely unconnected graphs where /Cn<,n = n fVom eqs.(29) and (32)... 

In order to formulate a distance matrix for unconnected graphs and digraphs, the distance between two vertices which are not connected by a wdk is defined as oo (in infinite simple graphs geodesics of infinite length may also occur). Hence, the distance matrix of a graph composed of two components, G Q U will exhibit the following block form ... 

An articulation point in a connected graph is a point whose removal breaks a graph into two or more unconnected parts such that at least one part contains no root point and at least one field point. (A slightly more general definition, which we will not need, is required to define an articulation point in a disconnected diagram.) This definition holds even when the graph has no root point or one root point. See Fig. 2 for illustrations of this definition. 

Figure 3.22 Molecular graphs show that (a) two unconnected macrocycles are considered to be the topological isomer of two linked macrocycles as the two situations cannot be interconverted without breaking bonds and (b) topological chirality can be imparted by molecular species becoming entangled.

A subgraph 5 is a set of elements from that bond graph that has no power bonds connected to any bond graph element outside the set. The subgraph may be connected to the rest of the bond graph by modulating signals or may be unconnected. 

Gn,u regroups all graphs with n vertices and m edges. To generate a graph sampled uniformly at random from the set one has to put m edges between vertex pairs chosen randomly from n initially unconnected vertices. 

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