کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4647842 1342380 2012 8 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Generalizations of Graham’s pebbling conjecture
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
Generalizations of Graham’s pebbling conjecture
چکیده انگلیسی

We investigate generalizations of pebbling numbers and of Graham’s pebbling conjecture that π(G□H)≤π(G)π(H)π(G□H)≤π(G)π(H), where π(G)π(G) is the pebbling number of the graph GG. We develop new machinery to attack the conjecture, which is now twenty years old. We show that certain conjectures imply others that initially appear stronger. We also find counterexamples that shows that Sjöstrand’s theorem on cover pebbling does not apply if we allow the cost of transferring a pebble from one vertex to an adjacent vertex to depend on the weight of the edge and we describe an alternate pebbling number for which Graham’s conjecture is demonstrably false.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 312, Issue 15, 6 August 2012, Pages 2286–2293
نویسندگان
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