منابع مشابه
Alliance free sets in Cartesian product graphs
Let G = (V,E) be a graph. For a non-empty subset of vertices S ⊆ V , and vertex v ∈ V , let δS(v) = |{u ∈ S : uv ∈ E}| denote the cardinality of the set of neighbors of v in S, and let S = V − S. Consider the following condition: δS(v) ≥ δS(v) + k, (1) which states that a vertex v has at least k more neighbors in S than it has in S. A set S ⊆ V that satisfies Condition (1) for every vertex v ∈ ...
متن کاملPacking Dimension, Hausdorff Dimension and Cartesian Product Sets
We show that the dimension adim introduced by R. Kaufman (1987) coincides with the packing dimension Dim, but the dimension aDim introduced by Hu and Taylor (1994) is different from the Hausdorff dimension. These results answer questions raised by Hu and Taylor. AMS Classification numbers: Primary 28A78, 28A80.
متن کاملOn unique minimum dominating sets in some Cartesian product graphs
Unique minimum vertex dominating sets in the Cartesian product of a graph with a complete graph are considered. We first give properties of such sets when they exist. We then show that when the first factor of the product is a tree, consideration of the tree alone is sufficient to determine if the product has a unique minimum dominating set.
متن کاملThe reliability Wiener number of cartesian product graphs
Reliability Wiener number is a modification of the original Wiener number in which probabilities are assigned to edges yielding a natural model in which there are some (or all) bonds in the molecule that are not static. Various probabilities naturally allow modelling different types of chemical bonds because chemical bonds are of different types and it is well-known that under certain condition...
متن کاملTHE CATEGORY OF T-CONVERGENCE SPACES AND ITS CARTESIAN-CLOSEDNESS
In this paper, we define a kind of lattice-valued convergence spaces based on the notion of $top$-filters, namely $top$-convergence spaces, and show the category of $top$-convergence spaces is Cartesian-closed. Further, in the lattice valued context of a complete $MV$-algebra, a close relation between the category of$top$-convergence spaces and that of strong $L$-topological spaces is establish...
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: Transactions of the American Mathematical Society
سال: 1976
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1976-0422587-6