An Improvement of the Godsil Bound
β Scribed by Akira Hiraki; Jack Koolen
- Book ID
- 105764613
- Publisher
- Springer
- Year
- 2002
- Tongue
- English
- Weight
- 106 KB
- Volume
- 6
- Category
- Article
- ISSN
- 0218-0006
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract The crossing number __cr__(__G__) of a simple graph __G__ with __n__ vertices and __m__ edges is the minimum number of edge crossings over all drawings of __G__ on the β^2^ plane. The conjecture made by ErdΕs in 1973 that __cr__(__G__)ββ₯β__Cm__^3^/__n__^2^ was proved in 1982 by Leighton
We show that the number of columns \(\left(c_{i}, a_{i}, b_{i}\right)=(1,1, k-2)\) in the intersection arrays of distance-regular graphs is at most three if the column \((1,0, k-1)\) exists. This improves the Bosheir-Nomura bound from four to three. 1994 Academic Press, Inc.