کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
396094 | 666193 | 2008 | 8 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Diameter variability of cycles and tori Diameter variability of cycles and tori](/preview/png/396094.png)
The diameter of a graph is an important factor for communication as it determines the maximum communication delay between any pair of processors in a network. Graham and Harary [N. Graham, F. Harary, Changing and unchanging the diameter of a hypercube, Discrete Applied Mathematics 37/38 (1992) 265–274] studied how the diameter of hypercubes can be affected by increasing and decreasing edges. They concerned whether the diameter is changed or remains unchanged when the edges are increased or decreased. In this paper, we modify three measures proposed in Graham and Harary (1992) to include the extent of the change of the diameter. Let D-k(G)D-k(G) is the least number of edges whose addition to G decreases the diameter by (at least) k , D+0(G)D+0(G) is the maximum number of edges whose deletion from G does not change the diameter, and D+k(G)D+k(G) is the least number of edges whose deletion from G increases the diameter by (at least) k . In this paper, we find the values of D-k(Cm)D-k(Cm), D-1(Tm,n)D-1(Tm,n), D-2(Tm,n)D-2(Tm,n), D+1(Tm,n)D+1(Tm,n), and a lower bound for D+0(Tm,n)D+0(Tm,n) where CmCm be a cycle with m vertices, Tm,nTm,n be a torus of size m by n.
Journal: Information Sciences - Volume 178, Issue 14, 15 July 2008, Pages 2960–2967