Detour Pebbling Number on Some Commutative Ring Graphs
DOI:
https://doi.org/10.26713/cma.v14i1.2018Keywords:
Pebbling number, Detour pebbling number, Zero-divisor, Sum and the product of zero-divisor graphAbstract
The detour pebbling number of a graph \(G\) is the least positive integer \(f^{*}(G)\) such that these pebbles are placed on the vertices of \(G\), we can move a pebble to a target vertex by a sequence of pebbling moves each move taking two pebbles off a vertex and placing one of the pebbles on an adjacent vertex using detour path. In this paper, we compute the detour pebbling number for the commutative ring of zero-divisor graphs, sum and the product of zero divisor graphs.
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D. F. Anderson and P. S. Livingston, The zero-divisor graph of a commutative ring, Journal of Algebra 217(2) (1999), 434 – 447, DOI: 10.1006/jabr.1998.7840.
R. A. Beeler, T. W. Haynes and R. Keaton, Domination cover rubbling, Discrete Applied Mathematics 260 (2019), 75 – 85, DOI: 10.1016/j.dam.2019.01.037.
J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, North-Holland, New York (1977), URL: https://www.zib.de/groetschel/teaching/WS1314/BondyMurtyGTWA.pdf.
G. Chartrand, Introductory Graph Theory, Dover Publications Inc., 320 pages (1985).
F. R. K. Chung, Pebbling in hypercubes, SIAM Journal on Discrete Mathematics 2(4) (1989), 467 – 472, DOI: 10.1137/0402041.
G. Hurlbert, A survey of graph pebbling, Congressus Numerantium 139 (1999), 41 – 64.
A. Lourdusamy and S. S. Nellainayaki, Detour pebbling in graphs, Advances in Mathematics: Scientific Journal 9(12) (2020), 10583 – 10589, DOI: 10.37418/amsj.9.12.44.
A. Lourdusamy and S. S. Nellainayaki, Detour pebbling on path related graphs, Advances in Mathematics: Scientific Journal 10(4) (2021), 2017 – 2024, DOI: 10.37418/amsj.10.4.16.
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