منابع مشابه
Domination 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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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.
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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...
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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...
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For a graph G, its rth power is constructed by placing an edge between two vertices if they are within distance r of each other. In this note we study the amount of edges added to a graph by taking its rth power. In particular we obtain that, for r ≥ 3, either the rth power is complete or “many” new edges are added. In this direction, Hegarty showed that there is a constant ǫ > 0 such e(G3) ≥ (...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1994
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)00480-f