Queens graphs for chessboards on the torus
نویسندگان
چکیده
Ve consider the independence, domination and independent domination numbers of graphs obtained from the moves of queens on chessboards drawn on the torus, and determine exact values for each of these parameters in infinitely many cases.
منابع مشابه
Some new results for the queens domination problem
Computing techniques are described which have resulted in the establishment of new results for the queens domination problem. In particular it is shown that the minimum cardinalities of independent sets of dominating queens for chessboards of size 14, 15, and 16 are 8, 9, and 9 respectively, and that the minimum cardinalities of sets of dominating queens for chessboards of size 29, 41, 45, and ...
متن کاملKaleidoscopes, Chessboards, and Symmetry
This paper describes the n-queens problem on an n × n chessboard. We discuss the possible symmetries of n-queens solutions and show how solutions to this classical chess question can be used to create examples of colorful artwork.
متن کاملUpper bounds for the domination numbers of toroidal queens graphs
We determine upper bounds for γ(Qn) and i(Qn), the domination and independent domination numbers, respectively, of the graph Qn obtained from the moves of queens on the n× n chessboard drawn on the torus.
متن کاملBalanced Black and White Coloring Problem on knights chessboards
Graph anticoloring problem is partial coloring problem where the main feature is the opposite rule of the graph coloring problem, i.e., if two vertices are adjacent, their assigned colors must be the same or at least one of them is uncolored. In the same way, Berge in 1972 proposed the problem of placing b black queens and w white queens on a n× n chessboard such that no two queens of different...
متن کاملOn the diagonal queens domination problem
It is shown that the problem of covering an n x n chessboard with a minimum number of queens on a major diagonal is related to the number-theoretic function rj(n), the smallest number of integers in a subset of {l,..., n} which must contain three terms in arithmetic progression. Several problems concerning the covering of chessboards by queens have been studied in the literature [2]. In this no...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 24 شماره
صفحات -
تاریخ انتشار 2001