Advances and Applications in Discrete Mathematics
Volume 27, Issue 1, Pages 105 - 122
(May 2021) http://dx.doi.org/10.17654/DM027010105 |
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SECURE DOMINATION COVER PEBBLING NUMBER FOR VARIANTS OF COMPLETE GRAPHS
S. Sarah Surya and Lian Mathew
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Abstract: A pebbling move is defined as the removal of two pebbles from any vertex and placing one on the adjacent vertex under a given configuration of pebbles on the vertices of a connected graph G. In this paper, we introduce a new graph invariant called the secure domination cover pebbling number which is a combination of cover pebbling and secure domination. The secure domination cover pebbling number, of a graph G is the minimum number of pebbles that must be placed on such that after a sequence of pebbling moves, the set of vertices with pebbles forms a secure dominating set regardless of the initial configuration. Also, we find the secure domination cover pebbling number for the complete graph the complete bipartite graph and the complete r-partite graph |
Keywords and phrases: graph pebbling, secure domination, cover pebbling number, secure domination cover pebbling number.
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