Graph disconnected

An articulation circle is a circle in a connected graph whose removal makes the graph disconnected, where at least one part contains no root point and at least one field point Arrows in Fig. 3 point to articulation circles. 

Conversely, a disconnected graph (null graph) coniains... 

Figure 6 The topological disconnectivity graph of alanine hexapeptide. (Adapted from Ref. 67.)...

If B— [bij] is an N xN matrix in which bu equals the degree of vertex i, bij = —1 if vertices i and j are adjacent and bij = 0 otherwise, then the number of spanning tree of G is equal to the determinant of any principal minor of B [hararybO]. The extremes occur for totally disconnected graphs that have no spanning trees and thus a complexity of zero, and for complete graphs of order N that contain the maximum possible number of distinct trees on N vertices. ... 

Other procedures for generating chains from polycyclic fused ring systems and for disconnecting fused rings which use simple graph theoretical approaches have been described.35 They make use of the dual of the molecular graph, i.e. the figure... 

The method can be illustrated with a simple example let us consider the diagram A which represents a pentacyclic fused system, as well as its dual in the graph theoretical sense. The thick lines are the "core bonds", as they were defined by mle 4. A strategic bond disconnection of the molecule can be effected as follows i) Select the ring which has the largest number of core bonds and at least one noncore bond. Disconnect a noncore bond which is exo to the adjacent ring (A... 

Compare, for instance, three possible disconnections of hirsutene (43) two proceeding according to the dual graph strategy (43 44 and 45) [24] [25], and... 

Disconnect the pH sensor and TI graphing calculator from the CBL unit. Following your teacher s directions, return all equipment to its proper place. 

N is the number of atoms, A and E are the adjacency and unit matrix, respectively, while s is the largest number of edges disconnected to each other in the acyclic graph. Thus, for Gx one obtains ... 

A graph is said to be vertex reducible, if it ca.n be cut into two disconnected pieces by cutting one vertex. 

The precise definition of the Hade potential needs a little more description. Thus, if an electrode containing a passive layer is allowed to float free (the potentiostat is disconnected) and its potential is measured and plotted against time, it will fall (become less positive) and then attain a plateau on the potential-time graph (Fig. 12.64). 

Fig. 6. Extrinsically non-planar homeomorphic figures a) a link (45) and the pair of disconnected circuit graphs (46) b) the trefoil knot shown as its mirror-images 47a and 47b...

The union GiUG2 is defined as the graph which vertex set is V,UV2 and edge set is E[UE2. A disconnected graph is a graph which can be expressed as the union of two graphs [54a]... 

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