Results 41 to 50 of about 7,067 (209)
Monotone Arithmetic Complexity of Graph Homomorphism Polynomials [PDF]
, 2022 We study homomorphism polynomials, which are polynomials that enumerate all homomorphisms from a pattern graph H to n-vertex graphs. These polynomials have received a lot of attention recently for their crucial role in several new algorithms for counting
Rahul, Chengot Sankaramenon +2 more
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On Weakly Distinguishing Graph Polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 A univariate graph polynomial P(G;X) is weakly distinguishing if for almost all finite graphs G there is a finite graph H with P(G;X)=P(H;X). We show that the clique polynomial and the independence polynomial are weakly distinguishing.
Johann A. Makowsky, Vsevolod Rakita
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From the Ising and Potts Models to the General Graph Homomorphism Polynomial
, 2016 A number of classical models in statistical physics, such as the Ising model, Potts model, and lattice gas, can be formulated in terms of the generating function for weighted versions of homo-morphisms from G to some graph H.
Klas Markström, Markström, Klas,
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The construction of graphs with irreducible matching polynomials and their generalizations
AKCE International Journal of Graphs and CombinatoricsThis paper investigates methods for constructing graphs whose matching polynomials are irreducible over [Formula: see text]. Building on this, the construction method is extended to general graph polynomials, for graphs whose polynomials satisfy certain ...
Hou Shengzhe
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On the dependence polynomial of a graph
European Journal of Combinatorics, 2007 For an \(n\)-vertex graph \(G\) and \(i=0, 1, \dots, n\), let \(c_i\) denote the number of complete subgraphs on \(i\) vertices in \(G\). The dependence polynomial \(P_G(z)\) of \(G\) is defined by \(P_G(z)=1+\sum_{i=1}^n (-1)^i c_iz^i\). Using a Möbius-type inversion formula, the authors show that \[ \begin{aligned} P_G(z)&=\sum_{\emptyset\not ...
Jianguo Qian, Andreas Dress, Yan Wang
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The chromatic polynomial of a graph [PDF]
Pacific Journal of Mathematics, 1985 First, the author summarizes some known results on chromatical polynomials and sketches their proofs. Then he lists the chromatical polynomials of all graphs with fewer than seven vertices.
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RC-Graphs and Schubert Polynomials [PDF]
Experimental Mathematics, 1993 Using a formula of Billey, Jockusch and Stanley, Fomin and Kirillov have introduced a new set of diagrams that encode the Schubert polynomials. We call these objects rc-graphs. We define and prove two variants of an algorithm for constructing the set of all rc-graphs for a given permutation.
Nantel Bergeron, Sara C. Billey
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On a class of polynomials associated with the Cliques in a graph and its applications
International Journal of Mathematics and Mathematical Sciences, 1989 The clique polynomial of a graph is defined. An explicit formula is then derived for the clique polynomial of the complete graph. A fundamental theorem and a reduction process is then given for clique polynomials.
E. J. Farrell
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Entropy and Multi-Fractal Analysis in Complex Fractal Systems Using Graph Theory
Axioms, 2023 In 1997, Sierpinski graphs, S(n,k), were obtained by Klavzar and Milutinovic. The graph S(1,k) represents the complete graph Kk and S(n,3) is known as the graph of the Tower of Hanoi. Through generalizing the notion of a Sierpinski graph, a graph named a
Zeeshan Saleem Mufti +3 more
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A Homomorphic Polynomial for Oriented Graphs
The Electronic Journal of Combinatorics, 2023 In this article, we define a function that counts the number of (onto) homomorphisms of an oriented graph. We show that this function is always a polynomial and establish it as an extension of the notion of chromatic polynomials. We study algebraic properties of this function.
Sandip Das 0001 +3 more
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