Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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PEBBLING ON THE MIDDLE GRAPH OF A COMPLETE BINARY TREE

  • LOURDUSAMY, A. (Department of Mathematics, St. Xavier's College (Autonomous), Affiliated to Manonmaniam Sundaranar University) ;
  • NELLAINAYAKI, S. SARATHA (Department of Mathematics, St. Xavier's College (Autonomous), Affiliated to Manonmaniam Sundaranar University) ;
  • STEFFI, J. JENIFER (Department of Mathematics, St. Xavier's College (Autonomous), Affiliated to Manonmaniam Sundaranar University)
  • Received : 2017.01.05
  • Accepted : 2019.05.15
  • Published : 2019.05.30
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Abstract

Given a distribution of pebbles on the vertices of a connected graph G, a pebbling move is defined as the removal of two pebbles from some vertex and the placement of one of those pebbles at an adjacent vertex. The t-pebbling number, $f_t(G)$, of a connected graph G, is the smallest positive integer such that from every placement of $f_t(G)$ pebbles, t pebbles can be moved to any specified vertex by a sequence of pebbling moves. A graph G has the 2t-pebbling property if for any distribution with more than $2f_t(G)$ - q pebbles, where q is the number of vertices with at least one pebble, it is possible, using the sequence of pebbling moves, to put 2t pebbles on any vertex. In this paper, we determine the t-pebbling number for the middle graph of a complete binary tree $M(B_h)$ and we show that the middle graph of a complete binary tree $M(B_h)$ satisfies the 2t-pebbling property.

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E1MCA9_2019_v37n3_4_163_f0001.png 이미지

Figure 1.1.

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