Panconnectivity of locally twisted cubes
نویسندگان
چکیده
The locally twisted cube LTQn which is a newly introduced interconnection network for parallel computing is a variant of the hypercube Qn . Yang et al. [X. Yang, G.M. Megson, D.J. Evans, Locally twisted cubes are 4-pancyclic, Applied Mathematics Letters 17 (2004) 919–925] proved that LTQn is Hamiltonian connected and contains a cycle of length from 4 to 2 n for n ≥ 3. In this work, we improve this result by showing that for any two different vertices u and v in LTQn (n ≥ 3), there exists a uv-path of length l with d(u, v)+ 2 ≤ l ≤ 2n − 1 except for a shortest uv-path. c © 2005 Elsevier Ltd. All rights reserved.
منابع مشابه
Node-pancyclicity and edge-pancyclicity of hypercube variants
Twisted cubes, crossed cubes, Möbius cubes, and locally twisted cubes are some of the widely studied hypercube variants. The 4-pancyclicity of twisted cubes, crossed cubes, Möbius cubes, locally twisted cubes and the 4-edgepancyclicity of crossed cubes are proven in [2, 1, 5, 10, 6] respectively. It should be noted that 4-edge-pancyclicity implies 4-node-pancyclicity which further implies 4-pan...
متن کاملConnectivity of Locally Exchanged Twisted Cubes∗
Connectivity κ(G) of a graph G is the minimum number of vertices whose removal leaves the remaining graph disconnected or trivial. This parameter is important for interconnection networks and can be used to measure reliability in such networks. In this paper, a new interconnection network called locally exchanged twisted cube (LETQ for short), denoted LeTQ(s, t), is proposed. We obtain some bas...
متن کاملConditional Diagnosability of the Locally Twisted Cubes under the PMC Model
In a multiprocessor systems, it is important to local and to replace the faulty processors to maintain systempsilas high reliability. The fault diagnosis, which is the process of identifying fault processors in a multiprocessor system through testing. The conditional diagnosis requires that for each processor u in a system, all the processors that are directly connected to u do not fail at the ...
متن کاملThe g-Good-Neighbor Conditional Diagnosability of Locally Twisted Cubes
In the work of Peng et al. in 2012, a new measure was proposed for fault diagnosis of systems: namely, g-good-neighbor conditional diagnosability, which requires that any faultfree vertex has at least g fault-free neighbors in the system. In this paper, we establish the g-good-neighbor conditional diagnosability of locally twisted cubes under the PMC model and the MM∗ model.
متن کاملA note on minimum linear arrangement for BC graphs
A linear arrangement is a labeling or a numbering or a linear ordering of the vertices of a graph. In this paper we solve the minimum linear arrangement problem for bijective connection graphs (for short BC graphs) which include hypercubes, Möbius cubes, crossed cubes, twisted cubes, locally twisted cube, spined cube, Z-cubes, etc. as the subfamilies.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Appl. Math. Lett.
دوره 19 شماره
صفحات -
تاریخ انتشار 2006