Loading...
| Friend's email | |
| Your name | |
| Your email | |
| enter code | |
This page was sent successfuly
- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 42592 (02)
- University: Sharif University of Thechnology
- Department: Mathematical Science
- Advisor(s): Akbari, Saeed
- Abstract:
- For an undirected graph G, a zero-sum flow is an assignment of non-zero real numbers on the edges of G such that the total sum of all edges incident with any vertex of G is zero. A zero-sum k-flow for a graph G is a zero-sum flow with labels from the set {±1, . . . , ±(k ? 1)}. In this thesis for a graph G, a necessary and sufficient condition forthe existence of zero-sum flow is given. It has been conjectured that if a graph G has azero-sumflow, then it has a zero-sum 6-flow. Also, it has been proved that this conjectureand Bouchet’s Conjecture for bidirected graphs are equivalent. It is shown that the con-jecture is true for 2-edge connected bipartite graphs, and every r-regular graph with r>2.Now, Let G be a graph, and ? be the smallest integer for which G has a nowhere-zero ?-flow, i.e., an integer ? for which G admits a nowhere-zero ?-flow, but it does not admit a (? ? 1)-flow. We denote the minimum flow number of G by ?(G). In this thesis, weshow that is ?(K ) ? 3 if m ? N, for i = 1, . . . , k and k ? 3. Also, we show thatm ,...,m i1 kif G and H are two arbitrary graphs and G has no isolated vertex, then ?(G ? H) ? 3,except two following cases:(i) One of the graphs G and H is K and another is 1-regular.2(ii) H = K and G is a graph with at least one isolated vertex or a component whose1every block is an odd cycle. Among other results, we prove that for every two graphs G and H with at least 4 vertices, ?(G ? H) ? 3
- Keywords:
- Nowhere Zero Flow ; Bipartite Graph ; Two Graph's Join ; Zero-sum Flow ; Minimum Flow Number ; Complete Multipartite Graph ; R-Regular Graph
Digital Object List
-
محتواي پايان نامه
- view
Bookmark