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Cited by 32 publications
(21 citation statements)
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“…While deciding connectivity is easy for circulant graphs, the exact calculation and minimization of the diameter of C D n are very difficult and well-studied problems even for the case |D| = 2 [1,11,12,25]. Many of the general upper and lower bounds on the diameter of circulant graphs easily generalize to distance graphs.…”
Section: Let Imentioning
confidence: 99%
“…While deciding connectivity is easy for circulant graphs, the exact calculation and minimization of the diameter of C D n are very difficult and well-studied problems even for the case |D| = 2 [1,11,12,25]. Many of the general upper and lower bounds on the diameter of circulant graphs easily generalize to distance graphs.…”
Section: Let Imentioning
confidence: 99%
“…Let n ≥ 5 be an integer with each prime factor congruent to 1 modulo 4, and let h be a solution to Geometrically, we may represent by a plane tessellation of squares [11,21,22] or an integer lattice [24]. See Figure 1 for an illustration.…”
Section: Optimal Routing and Gossipingmentioning
confidence: 99%
“…We obtain all x k easily once we find the minimum distance diagram. (c) In [24] an O(log n) algorithm for computing the diameter of any circulant graph of valency four was given. This can be used to compute the diameter d of .…”
Section: Optimal Routing and Gossipingmentioning
confidence: 99%
“…This serves as a mechanism for generating fixed-degree networks with desirable properties mirroring those of more densely connected chordal rings. On the negative side, determination of diameter and other topological parameters of chordal rings can be quite difficult [12], [39], [40]. Even for restricted classes of chordal rings such as the ones with a single skip type (degree 4), determination of topological properties is nontrivial in general and the problems have not yet been completely solved [13].…”
Section: Related Workmentioning
confidence: 99%