Perfect domination separation on square chessboard

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DOI:

https://doi.org/10.26637/MJM0804/0027

Abstract

This paper focuses on reducing the perfect domination number (γpf) of the chess pieces rooks, bishops and kings on an n×n board. Here we reduce this parameter by the separation problem which separates the board by placing a minimum number of chess pieces of a particular type with a minimum number of pawns. A subset D of V(G) is said to be a Perfect Dominating Set (PDS) if every vertex in VD is dominated by exactly one vertex of D. Among all the perfect dominating sets the cardinality of the one with the minimum number of vertices is the Perfect Domination Number (γpf).

Keywords:

Chessboard graphs, separation problem, perfect domination

Mathematics Subject Classification:

Mathematics
  • Pages: 1497-1501
  • Date Published: 01-10-2020
  • Vol. 8 No. 04 (2020): Malaya Journal of Matematik (MJM)

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Published

01-10-2020

How to Cite

K S P. Sowndarya, and Y. Lakshmi Naidu. “Perfect Domination Separation on Square Chessboard”. Malaya Journal of Matematik, vol. 8, no. 04, Oct. 2020, pp. 1497-01, doi:10.26637/MJM0804/0027.