Two-Disjoint-Cycle-Cover Pancyclicity of Dragonfly Networks

Zengxian Tian and Guanlin He ()
Additional contact information
Zengxian Tian: College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, China
Guanlin He: School of Computer and Software Engineering, Xihua University, Chengdu 610039, China

Mathematics, 2025, vol. 13, issue 23, 1-20

Abstract: Interconnection networks (often modeled as graphs) are critical for high-performance computing systems, as they have significant impact on performance metrics like latency and bandwidth. The dragonfly network, denoted as D ( n , r ) , is a promising topology owing to its modularity, low diameter, and cost-effectiveness. Ensuring reliability and efficiency in these networks requires robust cycle embedding properties. The two-disjoint-cycle-cover pancyclicity ensures that the network can be partitioned into two vertex-disjoint cycles of any feasible length. This suggests potential advantages for improving fault tolerance and load balancing strategies in interconnection networks. Formally, a graph G is called two-disjoint-cycle-cover [ a 1 , a 2 ] -pancyclic if for any integer ℓ satisfying a 1 ≤ 𝓁 ≤ a 2 , there exist two vertex-disjoint cycles C 1 and C 2 in G such that | V ( C 1 ) | = 𝓁 and | V ( C 2 ) | = | V ( G ) | − 𝓁 . While prior work has established Hamiltonicity and pancyclicity for D ( n , r ) , the two-disjoint-cycle-cover problem remains unexplored. This paper fills this gap by proving that D ( n , r ) is two-disjoint-cycle-cover [ 3 , | V ( D ( n , r ) ) | 2 ] -pancyclic with n ≥ 3 and r ≥ 2 , generalizing existing knowledge. Moreover, it can be obtained that D ( n , r ) is vertex-disjoint-cycle-coverable. Our proof employs a constructive method with case analysis, ensuring the existence of such cycles.

Keywords: dragonfly networks; pancyclicity; vertex-disjoint cycles; disjoint-cycle-cover; Hamiltonian (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/23/3736/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/23/3736/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:23:p:3736-:d:1799679

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().