منابع مشابه
Cartesian powers of graphs can be distinguished with two labels
The distinguishing number D(G) of a graph G is the least integer d such that there is a d-labeling of the vertices of G which is not preserved by any nontrivial automorphism. For a graph G let G be the rth power of G with respect to the Cartesian product. It is proved that D(G) = 2 for any connected graph G with at least 3 vertices and for any r ≥ 3. This confirms and strengthens a conjecture o...
متن کاملCartesian powers of graphs can be distinguished by two labels
1 The distinguishing number D(G) of a graph G is the least integer d such that there is a d-labeling 2 of the vertices of G which is not preserved by any nontrivial automorphism. For a graph G let Gr 3 be the r th power of G with respect to the Cartesian product. It is proved that D(Gr ) = 2 for any 4 connected graph G with at least 3 vertices and for any r ≥ 3. This confirms and strengthens a ...
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Parathyroid hormone (PTH) plays a vital role in regulating of blood Calcium. In addition, it regulates the amount of phosphate and vitamin D in the blood. PTH is a polypeptide hormone that found in the blood circulation as peptides with different amino acid counts. The active form of the PTH which has biological activity, contains 84 amino acids, but under the influence of proteolytic enzymes...
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Let A be a finitely generated domain of GK dimension less than 3 over a field K and let Q(A) denote the quotient division algebra of A. Using the ideas of Smoktunowicz, we show that if D is a finitely generated division subalgebras of Q(A) of GK dimension at least 2, then Q(A) is finite dimensional as a left D-vector space. We use this to show that if A is a finitely generated domain of GK dime...
متن کاملDomination number of graph fractional powers
For any $k in mathbb{N}$, the $k$-subdivision of graph $G$ is a simple graph $G^{frac{1}{k}}$, which is constructed by replacing each edge of $G$ with a path of length $k$. In [Moharram N. Iradmusa, On colorings of graph fractional powers, Discrete Math., (310) 2010, No. 10-11, 1551-1556] the $m$th power of the $n$-subdivision of $G$ has been introduced as a fractional power of $G$, denoted by ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1976
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1976-0392949-x