کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4949785 | 1364257 | 2017 | 9 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On a directed variation of the 1-2-3 and 1-2 Conjectures
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
نظریه محاسباتی و ریاضیات
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
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 uvâ verifying d+(u)=dâ(v)=1, is it possible to weight the arcs of D with weights among {1,2,3} so that, for every arc uvâ 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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Applied Mathematics - Volume 217, Part 2, 30 January 2017, Pages 123-131
Journal: Discrete Applied Mathematics - Volume 217, Part 2, 30 January 2017, Pages 123-131
نویسندگان
Emma Barme, Julien Bensmail, Jakub PrzybyÅo, Mariusz Woźniak,