Showing papers by "Huiqiu Lin published in 2014"
TL;DR: A sharp lower bound is obtained of g-extra edge-connectivity of an n-dimensional BC network for n ≥ 4 and 1 ≤ g ≤ 2[[n/2]].
Abstract: Reliability evaluation of interconnection network is important to the design and maintenance of multiprocessor systems. The extra connectivity and the extra edge-connectivity are two important parameters for the reliability evaluation of interconnection networks. The ${\mbi {n}}$ -dimensional bijective connection network (in brief, BC network) includes several well known network models, such as, hypercubes, Mobius cubes, crossed cubes, and twisted cubes. In this paper, we explore the extra connectivity and the extra edge-connectivity of BC networks, and discuss the structure of BC networks with many faults. We obtain a sharp lower bound of ${{g}}$ -extra edge-connectivity of an ${\mbi {n}}$ -dimensional BC network for ${{n}} \geq 4$ and $1 \leq { {g}} \leq {2^{[{{{n}} \over 2}]}}$ . We also obtain a sharp lower bound of ${ {g}}$ -extra connectivity of an ${{n}}$ -dimensional BC network for ${{n}} \geq 4$ and $1 \leq { {g}} \leq 2{ {n}}$ which improves the result in [“Reliability evaluation of BC networks,” IEEE Trans. Computers, DOI: 10.1109/tc.2012.106.] for $1 \leq { {g}} \leq { {n}} - 3$ . Furthermore, we give a remark about exploring the ${ {g}}$ -extra edge-connectivity of BC networks for the more general ${\mbi {g}}$ , and we also characterize the structure of BC networks with many faulty nodes or links. As an application, we obtain several results on the ${\mbi {g}}$ -extra (edge-) connectivity and the structure of faulty networks on hypercubes, Mobius cubes, crossed cubes, and twisted cubes.
68 citations
TL;DR: In this paper, it was shown that λ n − 1 (D (G ) ) ≤ − 1 if n ≥ 4 and λ N − 2 (D(G ) ≥ 2.5 when n ≥ 7, and that these graphs are determined by their distance spectra.
22 citations
TL;DR: Aouchiche et al. as discussed by the authors gave sharp upper and lower bounds on the largest and least eigenvalues of graphs when vertices are removed, and the extremal graph which attains the minimum smallest eigenvalue among all quasi-tree graphs is characterized.
Abstract: Let G = (V,E) be a simple graph with vertex set V (G) = {v1,v2,...,vn} and edge set E(G). In this paper, first some sharp upper and lower bounds on the largest and least eigenvalues of graphs are given when vertices are removed. Some conjectures in (M. Aouchiche. Comparaison Automatisee d'Invariants en Theorie des Graphes. Ph.D. Thesis, ´ Polytechnique de Montreal, February 2006.) and (M. Aouchiche, G. Caporossi, and P. Hansen. Variable neighborhood search for extremal graphs, 20. Automated comparison of graph invariants. MATCH Commun. Math. Comput. Chem., 58:365-384, 2007.) involving the spectral radius, diameter and matching number are also proved. Furthermore, the extremal graph which attains the minimum least eigenvalue among all quasi-tree graphs is characterized.
2 citations