Pancyclic And Hamiltonian Properties Of Dragonfly Networks

Abstract Dragonfly networks have significant advantages in data exchange due to the small network diameter, low cost and modularization. A graph $G$ is $vertex$-$pancyclic$ if for any vertex $u\in V(G)$, there exist cycles through $u$ of every length $\ell $ with $3\leq \ell \leq |V(G)|$. A graph $G$ is $Hamiltonian$-$connected$ if there exists a Hamiltonian path between any two distinct vertices $u,v\in V(G)$. In this paper, we mainly research the pancyclic and Hamiltonian properties of the dragonfly network $D(n,h)$, and find that it is Hamiltonian with $n\geq 1,\,\,h\geq 2$, pancyclic, vertex-pancyclic and Hamiltonian-connected with $n\geq 4,\,\,h\geq 2$.