Zero-Sum Flows in Regular Graphs
โ Scribed by S. Akbari; A. Daemi; O. Hatami; A. Javanmard; A. Mehrabian
- Publisher
- Springer Japan
- Year
- 2010
- Tongue
- English
- Weight
- 380 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0911-0119
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let D be a t- (v, k,k) design and let N i (D), for 1 โค i โค t, be the higher incidence matrix of D, a (0, 1)-matrix of size v iรb , where b is the number of blocks of D. A zero-sum flow of D is a nowhere-zero real vector in the null space of N 1 (D). A zero-sum k-flow of D is a zero-sum flow with val
A nowhere-zero 3-flow in a graph G is an assignment of a direction and a value of 1 or 2 to each edge of G such that, for each vertex v in G, the sum of the values of the edges with tail v equals the sum of the values of the edges with head v. Motivated by results about the region coloring of planar
## Abstract In this paper, we characterize graphs whose tensor product admit nowhereโzero 3โflow. The main result is: For two graphs __G__~1~ and __G__~2~ with ฮดโโฅโ2 and __G__~2~ not belonging to a wellโcharacterized class of graphs, the tensor product of __G__~1~ and __G__~2~ admits a nowhereโzero
## Abstract Let __G__ be a graph. For each vertex __v__ โ__V__(__G__), __N~v~__ denotes the subgraph induces by the vertices adjacent to __v__ in __G__. The graph __G__ is locally __k__โedgeโconnected if for each vertex __v__ โ__V__(__G__), __N~v~__ is __k__โedgeโconnected. In this paper we study t