Graph complete

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. ... 

Figure 1.9 shows that equation fi contains (is connected to) variables v and v2. The complete graph for the set of equations is shown in Figure 1.10. 

The complete graph of compressibility as a function of reservoir pressure is given in Figure 8-7. There is a discontinuity at the bubble point. The evolution of the first bubble of gas causes a large shift in the value of compressibility. Equation 8-7 applies at pressures above the bubble point, and Equation 8-24 applies at pressures below the bubble point. 

The special case rA = rB where all vertices are equidistant. The problem is therefore depicted by the complete graph Ki0 on ten vertices. This graph has genus seven and can therefore be embedded on the non-orientable surface with seven crosscaps. 

Therefore, searching for some edge-weighted maximal common subgraph for the two complete graphs is equivalent to searching for a clique [58] in this... 

As already said, at 4 loops there are 25 complete graphs with 11 different propagators, 17 of which without internal electron loops. The numbers of all the generated and independent topologies encountered when processing that... 

A complete graph is a graph in which every vertex is connected to every other vertex. For example, a complete graph having five vertices (represented by the symbol K5) is illustrated... 

A complete graph is a simple graph in which every pair of distinct vertices are adjacent. (Two vertices v and w of a graph G are said to be adjacent if there is an edge joining them the vertices v and w are then said to be incident to such an edge) [54a]... 

Fig. 1 K5. Top The complete graph on five vertices (left) and one-crossing presentation (right). Bottom Classical representations of K5 and the molecule made by Kuck and Schuster in 1988 [13], which has the same topology as K5...

A pictorial illustration of equivalent objects is depicted below where the individual elements occupy the edges of a complete graph ... 

The Z)/A index decreases as the cyclicity of the molecule increases, so that it reaches the maximum value for the monocyclic graph Ca and the minimum for the complete graph K, A being the number of vertices of the actual graph Ga- Therefore, a more suitable measure of molecular cyclicity was proposed as a standardized D/A index called the cyclicity index y ... 

A complete graph contains the maximal number of cycles and is denoted as Ka(<5), A being the number of vertices. 

The reference structure for Ptnin is the linear graph while for Pmax it is the - complete graph in which all atoms are bonded to each other their numerical values are calculated as follows ... 

A simple measure of structural complexity of a molecule based on its graph representation G compared with the parent -> complete graph K(Q, i.e. the complete graph with the same number of vertices. It is defined as ... 

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