Dominance of Rooks and Bishops in Fractal Chessboard

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2018 by IJMTT Journal
Volume-55 Number-5
Year of Publication : 2018
Authors : R.Sangeetha, G.Jayalalitha
  10.14445/22315373/IJMTT-V55P544

MLA

R.Sangeetha, G.Jayalalitha "Dominance of Rooks and Bishops in Fractal Chessboard", International Journal of Mathematics Trends and Technology (IJMTT). V55(5):340-344 March 2018. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

Abstract
This paper proves that a maximum of N - 2 non- attacking Rooks and N non- attacking Bishops can be placed in a N * N Fractal Chessboard (FC) which is defined as a board that grows progressively in a consistent manner using a 2 * 2 chessboard (B) by adding the copy of B to its sides and corners.

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Keywords
Rook Domination Number, Rook Independence Separation Number, Fractal Chessboard, Nonattacking Rook, Non- attacking Bishop.