On Coloring of graph fractional powers
نویسنده
چکیده
Let G be a simple graph. For any k ∈ N , the k−power of G is a simple graph G with vertex set V (G) and edge set {xy : dG(x, y) ≤ k} and the k−subdivision of G is a simple graph G 1 k , which is constructed by replacing each edge of G with a path of length k. So we can introduce the m−power of the n−subdivision of G, as a fractional power of G, that is denoted by G m n . In other words G m
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 ...
متن کاملColoring Graph Powers: Graph Product Bounds and Hardness of Approximation
We consider the question of computing the strong edge coloring, square graph coloring, and their generalization to coloring the k power of graphs. These problems have long been studied in discrete mathematics, and their “chaotic” behavior makes them interesting from an approximation algorithm perspective: For k = 1, it is well-known that vertex coloring is “hard” and edge coloring is “easy” in ...
متن کاملDistinguishing number and distinguishing index of natural and fractional powers of graphs
The distinguishing number (resp. index) $D(G)$ ($D'(G)$) of a graph $G$ is the least integer $d$ such that $G$ has an vertex labeling (resp. edge labeling) with $d$ labels that is preserved only by a trivial automorphism. For any $n in mathbb{N}$, the $n$-subdivision of $G$ is a simple graph $G^{frac{1}{n}}$ which is constructed by replacing each edge of $G$ with a path of length $n$...
متن کاملOn the Edge-Difference and Edge-Sum Chromatic Sum of the Simple Graphs
For a coloring $c$ of a graph $G$, the edge-difference coloring sum and edge-sum coloring sum with respect to the coloring $c$ are respectively $sum_c D(G)=sum |c(a)-c(b)|$ and $sum_s S(G)=sum (c(a)+c(b))$, where the summations are taken over all edges $abin E(G)$. The edge-difference chromatic sum, denoted by $sum D(G)$, and the edge-sum chromatic sum, denoted by $sum S(G)$, a...
متن کاملGraph 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 کاملOn colorings of graph fractional powers
For any k ∈ N, the k−subdivision of graph G is a simple graph G 1 k , which is constructed by replacing each edge of G with a path of length k. In this paper we introduce the mth power of the n−subdivision of G, as a fractional power of G, denoted by G m n . In this regard, we investigate chromatic number and clique number of fractional power of graphs. Also, we conjecture that χ(G m n ) = ω(G ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009