Affiliation:
1. Department of Mathematics, Hanseo University, Seosan 31962, Republic of Korea
2. Ewoo High School, Seongnam 13547, Republic of Korea
Abstract
The hypercube is one of the best models for the network topology of a distributed system. Recently, Padovan cubes and Lucas–Padovan cubes have been introduced as new interconnection topologies. Despite their asymmetric and relatively sparse interconnections, the Padovan and Lucas–Padovan cubes are shown to possess attractive recurrent structures. In this paper, we determine the cube polynomial of Padovan cubes and Lucas–Padovan cubes, as well as the generating functions for the sequences of these cubes. Several explicit formulas for the coefficients of these polynomials are obtained, in particular, they can be expressed with convolved Padovan numbers and Lucas–Padovan numbers. In particular, the coefficients of the cube polynomials represent the number of hypercubes, a symmetry inherent in Padovan and Lucas–Padovan cubes. Therefore, cube polynomials are very important for characterizing these cubes.
Funder
National Research Foundation of Korea
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
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