منابع مشابه
ON THE EDGE COVER POLYNOMIAL OF CERTAIN GRAPHS
Let $G$ be a simple graph of order $n$ and size $m$.The edge covering of $G$ is a set of edges such that every vertex of $G$ is incident to at least one edge of the set. The edge cover polynomial of $G$ is the polynomial$E(G,x)=sum_{i=rho(G)}^{m} e(G,i) x^{i}$,where $e(G,i)$ is the number of edge coverings of $G$ of size $i$, and$rho(G)$ is the edge covering number of $G$. In this paper we stud...
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توسیع تعدادی از نامساوی های چند جمله ای در مشتق قطبی
15 صفحه اولFactorization of the Characteristic Polynomial
We introduce a new method for showing that the roots of the characteristic polynomial of a finite lattice are all nonnegative integers. Our main theorem gives two simple conditions under which the characteristic polynomial factors in this way. We will see that Stanley’s Supersolvability Theorem is a corollary of this result. We can also use this method to demonstrate the factorization of a poly...
متن کاملThe matrix cover polynomial
The cover polynomial C(D) = C(D;x, y) of a digraph D is a twovariable polynomial whose coefficients are determined by the number of vertex coverings of D by directed paths and cycles. Just as for the Tutte polynomial for undirected graphs (cf. [11, 16]), various properties of D can be read off from the values of C(D;x, y). For example, for an n-vertex digraph D, C(D; 1, 0) is the number of Hami...
متن کاملComplexity of the Cover Polynomial
The cover polynomial introduced by Chung and Graham is a twovariate graph polynomial for directed graphs. It counts the (weighted) number of ways to cover a graph with disjoint directed cycles and paths, it is an interpolation between determinant and permanent, and it is believed to be a directed analogue of the Tutte polynomial. Jaeger, Vertigan, and Welsh showed that the Tutte polynomial is #...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1997
ISSN: 0095-8956
DOI: 10.1006/jctb.1997.1745