R. Duane Skaggs’s research while affiliated with Morehead State University and other places

... The global offensive k-alliance number γ o k (G) is the minimum cardinality among all global offensive k-alliances of G. In particular, γ o 1 (G) (respectively γ o 2 (G)) are known as the global (respectively strong) offensive alliance number of G [21,10]. ...

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Some results on the k-alliance and domination of graphs

... Chatham et al., in [2,5] defined the symmetric solutions such as ordinary, centrosymmetric, and doubly centrosymmetric solutions on a square board, and proved that all the solutions of N + k queens solutions belong to one of these symmetries. Using the studies done on separation problems on the square boards, this paper extends the work onto the rectangular boards. ...

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QUEENS INDEPENDENCE SEPARATION ON RECTANGULAR CHESSBOARDS

... The N-Queens problem is the placement of N queens on an N × N chessboard so that no queen can move to another queen's position in a single move. A placement in which any two attacking queens can be separated by a pawn is defined as a legal placement [4]. The Queens separation number s Q (M, N ) is the minimum number of pawns that can separate some legal placement of M queens on an N ×N board [4]. ...

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QUEENS INDEPENDENCE SEPARATION ON RECTANGULAR CHESSBOARDS

... One prominent area of research in this domain is the investigation of differentiating-dominating sets in graphs, which are alternatively referred to as identifying codes in certain contexts. This research has roots dating back to 1998 when Karpovsky, Chakrabarty, and Levitin introduced identifying codes (see [4]) and have been investigated further by Frick et al in 2008 (see [6]). Furthermore, in the study of Canoy and Malacas [12], they characterized the differentiating-dominating sets in the join, corona, and lexicographic product of graphs and determined the bounds or the exact differentiating-domination numbers of the aforementioned graphs. ...

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Differentiating Odd Dominating Sets in Graphs

... For example, Zhao determined that three pawns were necessary and sufficient to allow six independent queens on a 5 × 5 board [3]. Chatham et al. further explored the concept of placing pawns on a chessboard as obstacles in order to obtain "separated" chessboard graphs with altered graph parameters [4][5][6][7], with an emphasis on aspects of the "n + k queens problem" of finding arrangements of n + k independent queens and k pawns on an n × n chessboard. Only a few results were found regarding independence-separation on rook's and bishop's graphs. ...

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Some results for chessboard separation problems

... In [Cha09], given a chess piece C and a graph parameter π, the π-separation number s C (π, n, p) for C is defined as the minimum number of pawns for which some placement of those pawns on an n × n board will produce a board whose C graph has π = p. Following that pattern, we define the rooks diameter-separation number s R (diam, n, d) to be the minimum number of pawns for which some placement of those pawns on an n × n board will produce a board whose rooks graph has diameter d. ...

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Diameter-Separation of Chessboard Graphs