کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6871626 1440187 2018 5 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A note on a directed version of the 1-2-3 Conjecture
ترجمه فارسی عنوان
یک یادداشت در یک نسخه کارگردانی از خط 1-3-3
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نظریه محاسباتی و ریاضیات
چکیده انگلیسی
The least k such that a given digraph D=(V,A) can be arc-labeled with integers in the interval [1,k] so that the sum of values in-coming to x is distinct from the sum of values out-going from y for every arc (x,y)∈A, is denoted by χ̄Łe(D). This corresponds to one of possible directed versions of the well-known 1-2-3 Conjecture. Unlike in the case of other possibilities, we show that χ̄Łe(D) is unbounded in the family of digraphs for which this parameter is well defined. However, if the family is restricted by excluding the digraphs with so-called lonely arcs, we prove that χ̄Łe(D)≤4, and we conjecture that χ̄Łe(D)≤3 should hold.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Applied Mathematics - Volume 236, 19 February 2018, Pages 472-476
نویسندگان
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