Bibliographic Details
| Title: |
The orbits of Möbius cubes. |
| Authors: |
Liu, Jia-Jie1 (AUTHOR) jjliu@mail.shu.edu.tw |
| Source: |
Discrete Applied Mathematics. Aug2026, Vol. 389, p13-25. 13p. |
| Subjects: |
Hypercubes, Graph theory, Computer network architectures |
| Abstract: |
The M ö bius cube M Q n , a notable variant of the hypercube, is an interconnection network valued for its superior communication efficiency and low diameter. This paper investigates the network's structural homogeneity using the concept of graph orbits. The orbit number O r b (G) , which represents the number of distinct orbits that partition a graph's vertex set, provides a definitive measure of symmetry; O r b (G) = 1 signifies ideal structural equivalence (vertex-transitivity), as exemplified by the classic hypercube Q n. We demonstrate that while O r b (M Q n) = 1 for n ≤ 3 , this symmetry is lost in higher dimensions. Specifically, we prove that O r b (M Q 4) = 2 and O r b (M Q n) = 2 n − 2 for all n ≥ 5. This rapid growth in the orbit number demonstrates a critical lack of homogeneity for large n , highlighting a fundamental trade-off that severely complicates the SDN control plane and efficient load balancing. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
