Name
Abstract | ||
|---|---|---|
In this paper, we consider the following question, which stands as a directed analogue of the well-known 1-2-3 Conjecture: Given any digraph D with no arc u v ź verifying d + ( u ) = d - ( v ) = 1 , is it possible to weight the arcs of D with weights among { 1 , 2 , 3 } so that, for every arc u v ź of D , the sum of incident weights out-going from u is different from the sum of incident weights in-coming to v ? We answer positively to this question, and investigate digraphs for which even the weights among { 1 , 2 } are sufficient. In relation with the so-called 1-2 Conjecture, we also consider a total version of the problem, which we prove to be false. Our investigations turn to have interesting relations with open questions related to the 1-2-3 Conjecture. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1016/j.dam.2016.08.013 | Discrete Applied Mathematics |
Keywords | Field | DocType |
1-2-3 Conjecture,1-2 Conjecture,Digraphs | Discrete mathematics,Combinatorics,New digraph reconstruction conjecture,Conjecture,Collatz conjecture,Mathematics,Digraph | Journal |
Volume | Issue | ISSN |
217 | P2 | 0166-218X |
Citations | PageRank | References |
3 | 0.41 | 7 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Emma Barme | 1 | 3 | 0.41 |
| Julien Bensmail | 2 | 69 | 18.43 |
| Jakub Przybyło | 3 | 210 | 27.55 |
| Mariusz Woźniak | 4 | 204 | 34.54 |