On the largest eigenvalues of bipartite graphs which are nearly complete
โ Scribed by Yi-Fan Chen; Hung-Lin Fu; In-Jae Kim; Eryn Stehr; Brendon Watts
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 154 KB
- Volume
- 432
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
The pagenumber p(G) of a graph G is defined as the smallest n such that G can be embedded in a book with n pages. We give an upper bound for the pagenumber of the complete bipartite graph K m, n . Among other things, we prove p(K n, n ) w2nร3x+1 and p(K wn 2 ร4x, n ) n&1. We also give an asymptotic
In this paper all connected line graphs whose second largest eigenvalue does not exceed 1 are characterized. Besides, all minimal line graphs with second largest eigenvalue greater than 1 are determined.
## Abstract A short proof is given of the impossibility of decomposing the complete graph on __n__ vertices into __n__โ2 or fewer complete bipartite graphs.