Circles articulation

If an articulation circle is removed, the graph falls into 2 or more disconnected pieces, at least one of which contains no white circles. Take an arbitrary graph in the expansion of p2(l,2), say... 

In each of these graphs the white Zi-circle labeled 1 is an articulation circle. These graphs, along with all others with an articulation 1 circle, can be resummed to change the Zj-circle labeled 1 into a pj-circle. This process can be repeated for each articulation circle in a graph (both black circles and white circles), and hence p2(, 2) becomes... 

P2(U2) = the sum of all distinct simple graphs consisting of 2 white p,-circles, some or no black p,-circles, some or no /-bonds such that there is a path from each black circle to a white circle, and the graphs are free of articulation circles (2.1.23)... 

This is called the first replacement theorem. The set of graphs with z,-circles becomes the set of graphs with pj-circles and no articulation circles. 

A comparison of Eq. (106) and Fig. 11 with Eq. (103) and Fig. 9 shows immediately that the/ bond expansion of (T%) corresponds to those terms in Us+i)a that do not have a white articulation circle. An articulation circle is defined as a circle that, if removed, would cause the graph to fall apart into two or more pieces, at least one of which contains black circles but no white circles. Equation (108) is then equivalent to the following graphical prescription ... 

S/A = the sum of all distinct ALSC graphs with one white 1 circle labeled 0, one or more black z circles, and / bonds, n 2, such that the white circle is not an articulation circle... 

The sum in Eq. (109) consists of all connected graphs, with and without black articulation circles. Graphs that are free of articulation circles are called stars, 1-irreducible, or at least doubly connected (ALDC). 

Sfl (l. 2) + fa (l, 2) = the sum of all distinct simple connected graphs consisting of two white 1 circles labeled and 2/, one or more black p circles, f bonds of all possible orders greater than two, and /z bonds the graphs are free of articulation circles, and all black circles are interconnected by at least one route that does not include any white circles there is no pairwise bond between the white circles... 

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. 

An irreducible graph has no articulation circles. Graph c in Fig. 3 is an example of an irreducible graph. 

Turning circle for articulated vehicles to be 62 feet (26 meters) diameter minimum... 

In this sense, Nixon echoed what revisionist historians have shown to be Eisenhower s and Dulles s own inclinations toward a more realistic policy vis-a-vis Communist China. Moreover, Nixon went a little further in trying to articulate such a policy within official circles, and his arguments during this period foreshadowed some of the key elements of his later China policy. 

In the case of organic fanners in Ibiuna, the space for articulation and action is not solely the municipality of Ibiuna, or the circles of geographically proximate relations (i.e. neighbourhoods). The organic farmers in the study maintained complex relationships with diverse actors in wider networks relating to marketing, technical assistance, certification systems, and urban consumers. The... 

Figure 19 The active side chains are shown in (a). How the side chains are divided into biconnected components is illustrated in (b). Each side chain is numbered with a DEN (circle) and a low number (square next to corresponding residue). A difference between the DEN and the low number indicates the existence of an articulation point for the group of active sidechains. This image was adapted from Canutescu et al. ...

The trochoid Joint is composed of a ball shape that is surrounded by a circle composed of bone and ligaments. Its motion is primarily rotation. An example of this is the articulation between the adas and axis. 

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