We obtain upper and lower bounds on the average energy of circulant graphs with n vertices and regularity d. The average is taken over all representations of such graphs by circulant adjacency matrices.
On the energy of some circulant graphs
β Scribed by Igor Shparlinski
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 94 KB
- Volume
- 414
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract We investigate the conjecture that every circulant graph __X__ admits a __k__βisofactorization for every __k__ dividing |__E__(__X__)|. We obtain partial results with an emphasis on small values of __k__. Β© 2006 Wiley Periodicals, Inc. J Combin Designs 14: 406β414, 2006
Integral circulant graphs are a generalization of unitary Cayley graphs, recently studied by Klotz and Sander. The integral circulant graph X n (D) has vertices 0, 1, . . . , n -1, and two vertices a and b are adjacent iff gcd(xy, n) β D, where D β {d : Circulant graphs have various applications in
The distance energy of a graph G is a recently developed energy-type invariant, defined as the sum of absolute values of the eigenvalues of the distance matrix of G. There was a vast research for the pairs and families of non-cospectral graphs having equal distance energy, and most of these construc