Malaysian Journal of Mathematical Sciences, June 2026, Vol. 20, No. 2
Hamiltonicity in The Chained Cubic Tree Interconnection Network \(CCT(h,n)\)
Singh, R. A. D., Raj, A. Y. I
Corresponding Email: daisy.singh@sju.edu.in
Received date: 5 May 2025
Accepted date: 18 November 2025
Abstract:
Hamiltonicity plays a crucial role in the design of efficient interconnection networks, as it facilitates optimal routing of information between processors. The study of Hamiltonicity has inspired the development of several related concepts such as Hamiltonian laceability and Hamiltonian connectedness, fault tolerance and path covers etc., have lot of significance in computer networks as the presence of Hamiltonian path in network graphs is vital for addressing data communication challenges. A connected graph \(G\) is described as Hamiltonian\(-t_{\text{odd}}(t_{\text{even}})-\)laceable if for every pair of vertices \(x\) and \(y\), there exists a Hamiltonian path such that the distance \(d_{s}(x,y)=t \) where \(t\) is any odd (even) value satisfying \(1\leq t \leq Dm(G)\), with \(Dm (G)\) representing the graph's diameter. Furthermore, \(G\) is Hamiltonian\(-t-\)connected when it satisfies Hamiltonian\(-t-\)laceable condition for every \(t\) in the range \(1\leq t \leq Dm (G)\). This article examines the Hamiltonian \(t_{\text{odd}}-\)laceability and Hamiltonian t_{\text{even}}-\)laceability properties of a chained cubic tree interconnection network, denoted as \(CCT(h,n)\) specifically for \(h=1\), \(n \geq 2\). The study's findings emphasize the distance specific Hamiltonian\(-t-\)connectedness of \(CCT(h,n)\) characterized by \(d_{s}(x,y)=t\), for \(1\leq t\leq Dm(G)\).
Keywords: Hamiltonicity; Hamiltonian laceability; connectedness; laceability number.
