منابع مشابه
On Symmetry of Independence Polynomials
An independent set in a graph is a set of pairwise non-adjacent vertices, and α(G) is the size of a maximum independent set in the graph G. A matching is a set of non-incident edges, while μ(G) is the cardinality of a maximum matching. If sk is the number of independent sets of cardinality k in G, then I(G;x) = s0 + s1x+ s2x 2 + ...+ sαx , α = α (G) , is called the independence polynomial of G ...
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We prove the symmetry and unimodality of the independence polynomials of various graphs constructed by means of a recursive “path-like” construction. Our results provide a substantial generalization of the work of Zhu [Australas. J. Combin. 38 (2007), 27–33] and others.
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in this paper, we give a necessary and sufficient condition for the equality of two symmetrized decomposable polynomials. then, we study some algebraic and geometric properties of the induced operators over symmetry classes of polynomials in the case of linear characters.
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In this paper, we obtain the dimensions of symmetry classes of polynomials associated with the irreducible characters of the dihedral group as a subgroup of the full symmetric group. Then we discuss the existence of o-basis of these classes.
متن کاملOn the Stability of Independence Polynomials
The independence polynomial of a graph is the generating polynomial for the number of independent sets of each size and its roots are called independence roots. We investigate the stability of such polynomials, that is, conditions under which the independence roots lie in the left half-plane. We use results from complex analysis to determine graph operations that result in a stable or nonstable...
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ژورنال
عنوان ژورنال: Symmetry
سال: 2011
ISSN: 2073-8994
DOI: 10.3390/sym3030472