Atomic walk counts of negative order
István Lukovits1, Nenad Trinajstić
1Chemical Research Center, H-1525 Budapest, P.O.B. 17, Hungary. lukovits@chemres.hu
Abstract:
Atomic walk counts (awc's) of order k (k > or = 1) are the number of all possible walks of length k which start at a specified vertex (atom) i and end at any vertex j separated by m (0 < or = m < or = k) edges from vertex i. The sum of atomic walk counts of order k is the molecular walk count (mwc) of order k. The concept of atomic and molecular walk counts was extended to zero and negative orders by using a backward algorithm based on the usual procedure used to obtain the values of mwc's. The procedure can also be used in cases in which the adjacency matrix A related to the actual structure is singular and therefore A(-1) does not exist. awc's and mwc's of negative order may assume noninteger and even negative values. If matrix A is singular, atomic walk counts of zero order may not be equal to one.
Related Concept Videos
Atomic Structure
Radioactivity and Nuclear Equations
A nuclide of an element has a specific number of protons and...
Types of Radioactivity
Alpha (α) decay is the emission of an α particle from the nucleus. For example, polonium-210 undergoes α decay:
Nuclear Stability
To hold positively charged protons together in the...
Nuclear Transmutation
Atomic Structure


