The binary locating-dominating number of some convex polytopes
نویسندگان
چکیده
منابع مشابه
Identifying and Locating- Dominating Codes in Binary Hamming Spaces Identifying and Locating-Dominating Codes in Binary Hamming Spaces
Acknowledgements First of all I want to thank my supervisor Professor Iiro Honkala for his continuous support, and patience when long breaks in research took place. Many discussions with Iiro, his collaboration, suggestions for research topics, and careful proofreading made this work possible. I also want to thank Dr. Tero Laihonen for many inspiring discussions, suggestions for research topics...
متن کاملOn Locating-Dominating Codes in Binary Hamming Spaces
Let F = {0, 1} denote the binary field and F the n-dimensional Cartesian product of it. A code is a subset of F. The elements of F (resp. a code) are called words (resp. codewords) and the Hamming distance d(x, y) between two words x, y ∈ F is the number of coordinate positions in which they differ. The Hamming weight w(x) of a word x ∈ F is the number of 1’s in x. The minimum distance of a cod...
متن کاملEstimating the Number of Vertices in Convex Polytopes
Estimating the number of vertices of a convex polytope defined by a system of linear inequalities is crucial for bounding the run-time of exact generation methods. It is not easy to achieve a good estimator, since this problem belongs to the #P complexity class. In this paper we present two randomized algorithms for estimating the number of vertices in polytopes. The first is based on the well-...
متن کاملSome Aspects of the Combinatorial Theory of Convex Polytopes
We start with a theorem of Perles on the k-skeleton, Skel k (P) (faces of dimension k) of d-polytopes P with d+b vertices for large d. The theorem says that for xed b and d, if d is suuciently large, then Skel k (P) is the k-skeleton of a pyramid over a (d ? 1)-dimensional polytope. Therefore the number of combinatorially distinct k-skeleta of d-polytopes with d + b vertices is bounded by a fun...
متن کاملThe locating chromatic number of the join of graphs
Let $f$ be a proper $k$-coloring of a connected graph $G$ and $Pi=(V_1,V_2,ldots,V_k)$ be an ordered partition of $V(G)$ into the resulting color classes. For a vertex $v$ of $G$, the color code of $v$ with respect to $Pi$ is defined to be the ordered $k$-tuple $c_{{}_Pi}(v)=(d(v,V_1),d(v,V_2),ldots,d(v,V_k))$, where $d(v,V_i)=min{d(v,x):~xin V_i}, 1leq ileq k$. If distinct...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Ars Mathematica Contemporanea
سال: 2017
ISSN: 1855-3974,1855-3966
DOI: 10.26493/1855-3974.973.479