منابع مشابه
Acyclic orientations of graphs
Let G be a finite graph with p vertices and x its chromatic polynomial. A combinatorial interpretation is given to the positive integer (-l)px(-A), where h is a positive integer, in terms of acyclic orientations of G. In particular, (-l)Px(-1) is the number of acyclic orientations of G. An application is given to the enumeration of labeled acyclic digraphs. An algebra of full binomial type, in ...
متن کامل1)-orientations of graphs
Article history: Received 10 July 2006 Available online 29 August 2008
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We consider the problem of determining the maximum and the minimum number of upward planar orientations a maximal planar graph can have. We show that n-vertex maximal planar graphs have at least Ω(n · 1.189) and at most O(n · 4) upward planar orientations. Moreover, there exist n-vertex maximal planar graphs having as few as O(n · 2) upward planar orientations and n-vertex maximal planar graphs...
متن کاملLine graphs associated to the maximal graph
Let $R$ be a commutative ring with identity. Let $G(R)$ denote the maximal graph associated to $R$, i.e., $G(R)$ is a graph with vertices as the elements of $R$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $R$ containing both. Let $Gamma(R)$ denote the restriction of $G(R)$ to non-unit elements of $R$. In this paper we study the various graphi...
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Bounds for the chromatic number and for some related parameters of a graph are obtained by applying algebraic techniques. In particular, the following result is proved: If G is a directed graph with maximum outdegree d, and if the number of Eulerian subgraphs of G with an even number of edges differs from the number of Eulerian subgraphs with an odd number of edges then for any assignment of a ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Linear Algebra
سال: 2020
ISSN: 1081-3810
DOI: 10.13001/ela.2020.5217