Complete normality of cartesian products
نویسندگان
چکیده
منابع مشابه
Distinguishing colorings of Cartesian products of complete graphs
We determine the values of s and t for which there is a coloring of the edges of the complete bipartite graph Ks,t which admits only the identity automorphism. In particular this allows us to determine the distinguishing number of the Cartesian product of complete graphs. The distinguishing number of a graph is the minimum number of colors needed to label the vertices so that the only color pre...
متن کاملDistinguishing numbers of Cartesian products of multiple complete graphs
We examine the distinguishing number of the Cartesian product of an arbitrary number of complete graphs. We show that for u1 ≤ · · · ≤ ud the distinguishing number of the Cartesian product of complete graphs of these sizes is either du d e or du 1/s d e + 1 where s = Πd−1 i=1 ui. In most cases, which of these values it is can be explicitly determined.
متن کاملThe distinguishing number of Cartesian products of complete graphs
The distinguishing number D(G) of a graph G is the least integer d such that G has a labeling with d labels that is preserved only by a trivial automorphism. We prove that Cartesian products of relatively prime graphs whose sizes do not differ too much can be distinguished with a small number of colors. We determine the distinguishing number of the Cartesian product Kk ¤Kn for all k and n, eith...
متن کاملCritical groups for complete multipartite graphs and Cartesian products of complete graphs
The critical group of a connected graph is a finite abelian group, whose order is the number of spanning trees in the graph, and which is closely related to the graph Laplacian. Its group structure has been determined for relatively few classes of graphs, e.g. complete graphs, and complete bipartite graphs. For complete multipartite graphs Kn1,...,nk , we describe the critical group structure c...
متن کاملCondensations of Cartesian products
We consider when one-to-one continuous mappings can improve normalitytype and compactness-type properties of topological spaces. In particular, for any Tychonoff non-pseudocompact space X there is a μ such that X can be condensed onto a normal (σ-compact) space if and only if there is no measurable cardinal. For any Tychonoff space X and any cardinal ν there is a Tychonoff space M which preserv...
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: Fundamenta Mathematicae
سال: 1948
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-35-1-271-274