منابع مشابه
Graph Powers and Graph Homomorphisms
In this paper we investigate some basic properties of fractional powers. In this regard, we show that for any rational number 1 ≤ 2r+1 2s+1 < og(G), G 2r+1 2s+1 −→ H if and only if G −→ H− 2s+1 2r+1 . Also, for two rational numbers 2r+1 2s+1 < 2p+1 2q+1 and a non-bipartite graph G, we show that G 2r+1 2s+1 < G 2p+1 2q+1 . In the sequel, we introduce an equivalent definition for circular chromat...
متن کاملMeasure preserving homomorphisms and independent sets in tensor graph powers
In this note, we study the behavior of independent sets of maximum probability measure in tensor graph powers. To do this, we introduce an upper bound using measure preserving homomorphisms. This work extends some previous results about independence ratios of tensor graph powers.
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 ...
متن کاملOn Powers of Some Graph Operations
Let $G*H$ be the product $*$ of $G$ and $H$. In this paper we determine the rth power of the graph $G*H$ in terms of $G^r, H^r$ and $G^r*H^r$, when $*$ is the join, Cartesian, symmetric difference, disjunctive, composition, skew and corona product. Then we solve the equation $(G*H)^r=G^r*H^r$. We also compute the Wiener index and Wiener polarity index of the skew product.
متن کاملGraph Powers
The investigation of the asymptotic behaviour of various parameters of powers of a fixed graph leads to many fascinating problems, some of which are motivated by questions in information theory, communication complexity, geometry and Ramsey theory. In this survey we discuss these problems and describe the techniques used in their study which combine combinatorial, geometric, probabilistic and l...
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: The Electronic Journal of Combinatorics
سال: 2010
ISSN: 1077-8926
DOI: 10.37236/289