Dual graph

It is significant that both V- and D-tessellations are unequivocally interrelated because they form geometrically dual graphs. For a brief expression of a relation between these two lattices let us designate a total number of facets in V- and D-lattices as/yE and E, and the total number of edges as BV1 and liV) z, respectively. For dual graphs the relation is [100,146,147]... 

Application of Corey s rules to polycyclic fused ring structures. The dual graph procedure... 

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

For a connected plane graph G, denote its plane dual graph by G and define it on the set of faces of G with two faces being adjacent if they share an edge. Clearly, v(G ) = p(G) and p(G ) = v(G). 

SeSe96] B. Servatius and H. Servatius, Self-dual graphs, Discrete Mathematics 149-1 3 (1996) 223-232. 

A member of a family characterized by a self-dual graph can define a structure that has a different space group than that of each skeletal graph, by considering the region between the surfaces H = h and H =—h to be the region of unit density. We have seen that the transformation (m, i , — u, 1 — u, 1 — w) takes a surface S with H = — h—positive with... 

Table 3.1 Topological characterization of the 200 nodes of the reference dual graphene lattice when a SW defect is present. Nodes are sorted by their w,- values. Dual graph is made of 200 vertices with W = 116,015 Af = 10 total bonds in the graph B = 600 summing bn entries gives B value twice sum of >v, values is W. The most stable vertices are the two heptagons V91, Vlll on the contrary the two adjacent pentagons V90, V92 are the less stable ones...

In Eigure 13.4, we show dual graphs of the four-color maps representing (the first exon of p-globin gene of) for the nine species listed in Table 13.2. The four-color maps and their dual graphs are based on the square grid as a template. In Table 13.4,... 

Absolute Magnitudes of Four Nonzero Eigenvalues of the "Squared" Euclidean Distance Matrices Associated with the Dual Graphs Representing the Nine Species... 

Plot a dual graph of global temperature and global atmospheric levels of carbon dioxide on the vertical axis against year. 

We present an approximate algorithm, based on the Voronoi diagram of the terrain, which is a variant of the popular retraction algorithm [14], We then present algorithms that operate on dual graphs... 

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