caa a22 4500 475778251 CHVBK 20180406123637.0 cr unu---uuuuu 170329e20000601xx s 000 0 eng 10.1007/PL00021179 doi (NATIONALLICENCE)springer-10.1007/PL00021179 The 2-Pebbling Property and a Conjecture of Graham's [Elektronische Daten] [Hunter S. Snevily, James A. Foster] Abstract. : The pebbling number of a graph G, f(G), is the least m such that, however m pebbles are placed on the vertices of G, we can move a pebble to any vertex by a sequence of moves, each move taking two pebbles off one vertex and placing one on an adjacent vertex. It is conjectured that for all graphs G and H, f(G×H)≤f(G)f(H).¶Let C m and C n be cycles. We prove that f(C m×C n)≤f(C m) f(C n) for all but a finite number of possible cases. We also prove that f(G×T)≤f(G) f(T) when G has the 2-pebbling property and T is any tree. Springer-Verlag Tokyo, 2000 Snevily Hunter S. Department of Mathematics and Statistics, University of Idaho, Moscow, ID 83844-0101, USA. e-mail: snevily@uidaho.edu, US aut Foster James A. Department of Computer Science, University of Idaho, Moscow, ID 83844-0101, USA e-mail: foster@cs.uidaho.edu, US aut https://doi.org/10.1007/PL00021179 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/PL00021179 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Snevily Hunter S. Department of Mathematics and Statistics, University of Idaho, Moscow, ID 83844-0101, USA. e-mail: snevily@uidaho.edu, US aut NATIONALLICENCE 700 1- Foster James A. Department of Computer Science, University of Idaho, Moscow, ID 83844-0101, USA e-mail: foster@cs.uidaho.edu, US aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer