A COMPREHENSIVE REVIEW ON GRAPH PEBBLING AND RUBBLING

Abstract

Abstract A graph pebbling is a combinatorial game played over a fixed graph and a pebbling move is the method of removing two pebbles from one endpoint and sets one pebble at the other endpoint, while the remaining pebble is dropped. A graph’s rubbling number is the smallest number necessary to ensure that any vertex can be reached from any pebble distribution of pebbles. A vertex is reachable if a pebble can be placed using pebbling or rubbling moves. In this paper we have attempted to give a summary of how graph pebbling have undergone a lot of challenges to derive many strong results in proof complexity. A comprehensive review of the existing works in pebbling and rubbling is carried out in a sequential order.