The circulant G,(al,. . . , ak), where 0 < al < ... < a k < ( n + 1 ) / 2 , is defined as the vertex-transitive graph that has vertices ifal,. . . ,if a k (mod n) adjacent to each vertex i. In this work we show that the connected circulants of degree at least three contain all even cycles. In additi
Reliability analysis of circulant graphs
β Scribed by Li, Qiaoliang; Li, Qiao
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 82 KB
- Volume
- 31
- Category
- Article
- ISSN
- 0028-3045
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β¦ Synopsis
The circulant graphs are of particular interest as models of communication networks. In this work, we present new reliability analysis results for circulants based on the concept of restricted edge connectivity, which generalizes the super-l property of a graph. We evaluate the restricted edge connectivity l and the number of i-cutsets N i (G), l Β°i Γ΅ l, for any circulant graph explicitly. This improves the previous results on the subject.
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A computation task running in distributed systems can be represented as a directed graph H(V, E) whose vertices and edges may fail with known probabilities. In this paper, we introduce a reliability measure, called the distributed task reliability, to model the reliability of such computation tasks.
The following asymptotic estimation of the maximum number of spanning trees f k (n) in 2kregular circulant graphs ( k ΓΊ 1) on n vertices is the main result of this paper: )) , where