Adjacency matrix branch

Bertz branching index connection number - edge adjacency matrix... 

Ngs) [Gordon and Scantlebury, 1964] or Bertz branching index Bl), is the simplest graph-invariant obtained from the edge adjacency matrix which considers both vertices and edges and is calculated as ... 

The molecular walk count is related to molecular branching and size and in general to the molecular complexity of the graph. It was found that mmfi is directly related to the Lovasz-Pelikan index, that is, the largest eigenvalue of the adjacency matrix [Cvetkovic and Gutman, 1977]. 

Can we interpret the first eigenvalue of a D/D matrix The first eigenvalue of the adjacency matrix of trees has already been suggested as an index of molecular branching. Recently it was suggested that the first eigenvalue of the resonance... 

FIGURE 9. Comparison of the observed ionization energies 7 of the C2s bands in the He(IIa) PE spectra of linear, branched and monocyclic hydrocarbons with the lowest eigenvalues (equation 38) obtained by diagonalizing the adjacency matrix A of the corresponding AR-models (cf equation 39). Normal alkanes C , n = 1 to 5, methane to pentane. Branched alkanes i-C = isobutane, 1-C5 = isopentane, neo-Cs = neopentane. Cycloalkanes C , n = 3 to 8, cyclopropane to cyclooctane... 

Branched topologies as generated by the conditional Monte Carlo methods described in this section are most conveniently represented in matrix forms from graph theory [33, 53]. We name two of them the adjacency matrix A and the incidence matrix C (see Figure 9.22). They both describe connectivity. Note that in... 

Traditionally, laminate strength theories are based on ply strengths and models that use them to predict when a laminate would fail. The complexities associated with failure of a single ply are compounded in this case by the fact that damage created in one ply can interact with damage in other plies and evolve very differently depending on the laminate. For example, matrix cracks may evolve to delaminations or may branch out to adjacent plies as shown in Figure 6.6. 

Figure 6.6 Matrix cracks triggering delaminations versus matrix cracks branching into other matrix cracks in adjacent plies.

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