Cover Pebbling Number of Some Cycle Related Graphs

2019 ◽  
Vol 10 (6) ◽  
pp. 1322-1331
Author(s):  
Joice Punitha M ◽  
Suganya A
Keyword(s):  
2019 ◽  
Vol 342 (7) ◽  
pp. 2148-2157 ◽  
Author(s):  
Ervin Győri ◽  
Gyula Y. Katona ◽  
László F. Papp ◽  
Casey Tompkins

2019 ◽  
Vol 11 (06) ◽  
pp. 1950068
Author(s):  
Nopparat Pleanmani

A graph pebbling is a network optimization model for the transmission of consumable resources. A pebbling move on a connected graph [Formula: see text] is the process of removing two pebbles from a vertex and placing one of them on an adjacent vertex after configuration of a fixed number of pebbles on the vertex set of [Formula: see text]. The pebbling number of [Formula: see text], denoted by [Formula: see text], is defined to be the least number of pebbles to guarantee that for any configuration of pebbles on [Formula: see text] and arbitrary vertex [Formula: see text], there is a sequence of pebbling movement that places at least one pebble on [Formula: see text]. For connected graphs [Formula: see text] and [Formula: see text], Graham’s conjecture asserted that [Formula: see text]. In this paper, we show that such conjecture holds when [Formula: see text] is a complete bipartite graph with sufficiently large order in terms of [Formula: see text] and the order of [Formula: see text].


2005 ◽  
Vol 296 (1) ◽  
pp. 15-23 ◽  
Author(s):  
Betsy Crull ◽  
Tammy Cundiff ◽  
Paul Feltman ◽  
Glenn H. Hurlbert ◽  
Lara Pudwell ◽  
...  
Keyword(s):  

Author(s):  
Chin-Lin Shiue ◽  
Hung-Hsing Chiang ◽  
Mu-Ming Wong ◽  
H. M. Srivastava
Keyword(s):  

2020 ◽  
Vol 12 (05) ◽  
pp. 2050071
Author(s):  
A. Lourdusamy ◽  
T. Mathivanan

The [Formula: see text]-pebbling number, [Formula: see text], of a connected graph [Formula: see text], is the smallest positive integer such that from every placement of [Formula: see text] pebbles, [Formula: see text] pebbles can be moved to any specified target vertex by a sequence of pebbling moves, each move taking two pebbles off a vertex and placing one on an adjacent vertex. A graph [Formula: see text] satisfies the [Formula: see text]-pebbling property if [Formula: see text] pebbles can be moved to any specified vertex when the total starting number of pebbles is [Formula: see text], where [Formula: see text] is the number of vertices with at least one pebble. We show that the cycle [Formula: see text] satisfies the [Formula: see text]-pebbling property. Herscovici conjectured that for any connected graphs [Formula: see text] and [Formula: see text], [Formula: see text]. We prove Herscovici’s conjecture is true, when [Formula: see text] is an even cycle and for variety of graphs [Formula: see text] which satisfy the [Formula: see text]-pebbling property.


2014 ◽  
Vol 8 ◽  
pp. 4275-4283
Author(s):  
Michael E. Subido ◽  
Imelda S. Aniversario
Keyword(s):  

2012 ◽  
Vol 312 (15) ◽  
pp. 2401-2405 ◽  
Author(s):  
Johan Björklund ◽  
Cecilia Holmgren
Keyword(s):  

2012 ◽  
Vol 312 (21) ◽  
pp. 3174-3178 ◽  
Author(s):  
Yongsheng Ye ◽  
Mingqing Zhai ◽  
Yun Zhang
Keyword(s):  

Author(s):  
Chin-Lin Shiue ◽  
Hung-Hsing Chiang ◽  
Mu-Ming Wong ◽  
H. M. Srivastava
Keyword(s):  

2020 ◽  
Vol 8 ◽  
Author(s):  
Zheng-Jiang Xia ◽  
Zhen-Mu Hong
Keyword(s):  

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