OPTIMAL PEBBLING OF COMPLETE BINARY TREES AND A META-FIBONACCI SEQUENCE

被引：0
|
作者：
Lewis, Thomas M. [1 ]
Salinas, Fabian [2 ]
机构：
[1] Furman Univ, Dept Math, Greenville, SC 29613 USA
[2] Vanderbilt Univ, Dept Math, Nashville, TN 37212 USA
来源：
DISCUSSIONES MATHEMATICAE GRAPH THEORY | 2024年
关键词：
optimal pebbling; complete binary tree; meta-Fibonacci sequence; NUMBER; DOMINATION; GRAPHS;
D O I：
10.7151/dmgt.2556
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In 1999, Fu and Shiue published a paper on optimal pebblings of complete m-ary trees. Among other things, they produced OPCBT, an integer linear program that produces an optimal pebbling of a complete binary tree. Building upon their work, we give an explicit representation of the optimal pebbling number of a complete binary tree. Among other things, we show that the sequence of optimal pebbling numbers of complete binary trees indexed by their heights is related to the Conolly sequence, a type of meta-Fibonacci sequence.
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页数：14
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