Total walk count

The total walk count 7WC is the total number of walks of any length in the graph and is calculated as ... 

The total walk count is a measure of the molecular complexity, increasing both with increasing size and branching. 

The molecular walk count of length Z (in M or in M ) was mentioned several times. It adds all entries of the Z-th power of the bond matrix of M or of M. These indices were introduced by C. and G. Rucker [264], they describe the complexity [269] of a (molecular) graph. Walk counts are mostly evaluated for the H-suppressed molecule. The total walk count sums molecular walk counts of all lengths Z ... 

In the case of M = A, the global walk number Wa is just the - molecular walk count of fcth order i.e. the total number of length k walks in the graph. 

The molecular self-retuming walk count of kth order is the total number of self-returning walks of length k in the graph and is simply calculated by summing up all of the atomic selfreturning walk counts of the same order... 

The molecular walk count mwe of length k (also called walk number or graph walk count, GWe ) is the total number of walks of length k in the molecular graph and, for any k different from zero, it is calculated as the half sum of all atomic walk counts of the same length k, that is, as the half sum of the entries in each column of the SW matrix ... 

This just counts the total number of monomers at real-space position r. To calculate the correlation function, use the fact that for a Gaussian, random walk ... 

Total number of walks. All translationally inequivalent n-step SAW are counted. These may occur anywhere in the lattice. This number is bigger than the number of fixed origin walks, and by definition, takes into account vertices over the whole tiling. 

This connection is a fundamental one and it can be expected to operate more generally for other types of quantities. Indeed, the same type of relationship can be postulated for the electron lifetime, as shown recently by Ansari-Rad et al. [13, 56], On the one hand, the small perturbation lifetime is related to the decay of the Fermi level after injection of excess carriers. On the other hand a jump lifetime tj can be calculated by Monte Carlo simulation by following the survival time of a specific carrier that undergoes the sequence of events indicated in Fig. 11b, i.e., random walk in the total DOS and charge transfer to acceptor species in the electrolyte, tj is different from the free carrier lifetime, Tf, introduced above, in that the latter takes into account the siuwival time of a free carrier, just by the charge transfer mechanism, without counting the prior random walk. In fact T corresponds to the free electrons diffusion coefficient in the diffusion formalism, Dq. The relationship between these two lifetime quantities is given by [13]... 

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