We give a matrix generalization of the family of exponential polynomials in one variable , k (x). Our generalization consists of a matrix of polynomials 8 k (X)= (8 (k) i, j (X)) n i, j=1 depending on a matrix of variables X=(x i, j ) n i, j=1 . We prove some identities of the matrix exponential pol
Computer enumeration of walks on directed graphs
β Scribed by K. Balasubramanian
- Publisher
- John Wiley and Sons
- Year
- 1991
- Tongue
- English
- Weight
- 526 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0192-8651
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β¦ Synopsis
A vectorized computer code is developed for the enumeration of walks through the matrix power method for directed graphs. Application of this code to several graphs is considered. It is shown that the coefficients in the generating functions for signed graphs are much smaller in magnitude. It is shown that self-avoiding walks on some graphs can be enumerated as a linear combination of walk GFs of directed paths and rooteddirected paths.
π SIMILAR VOLUMES
The computer code developed previously (K. Balasubramanian, J . Computational Chern., 5,387 (1984)) for the characteristic polynomials of ordinary (nonweighted) graphs is extended in this investigation to edge-weighted graphs, heterographs (vertex-weighted), graphs with loops, directed graphs, and s
A method is described for calculating the mean cover time for a particle performing a simple random walk on the vertices of a finite connected graph. The method also yields the variance and generating function of the cover time. A computer program is available which utilises the approach to provide