Record number :
1455875
Title of article :
Bounds on the Rubbling and Optimal Rubbling Numbers of Graphs
Author/Authors :
Katona، نويسنده , , Gyula Y. and Sieben، نويسنده , , Nلndor، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2011
Pages :
6
From page :
487
To page :
492
Abstract :
A pebbling move on a graph removes two pebbles at a vertex and adds one pebble at an adjacent vertex. Rubbling is a version of pebbling where an additional move is allowed. In this new move, one pebble each is removed at vertices v and w adjacent to a vertex u, and an extra pebble is added at vertex u. A vertex is reachable from a pebble distribution if it is possible to move a pebble to that vertex using rubbling moves. The rubbling number is the smallest number m needed to guarantee that any vertex is reachable from any pebble distribution of m pebbles. The optimal rubbling number is the smallest number m needed to guarantee a pebble distribution of m pebbles from which any vertex is reachable. We give bounds for rubbling and optimal rubbling numbers.
Keywords :
pebbling , bounded diameter , rubbling
Journal title :
Electronic Notes in Discrete Mathematics
Link To Document :