Related papers: Mathematical results on harmonic polynomials
In this article, we focus on the characteristic polynomial of a graph containingloops, but without multiple edges. We present a relationship between thecharacteristic polynomial of a graph with loops and the graph obtained byremoving all…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
Symmetric edge polytopes are a recent and well-studied family of centrally symmetric polytopes arising from graphs. In this paper, we introduce a generalization of this family to arbitrary simplicial complexes. We show how topological…
In this work we provide a novel approach for computing the coefficients of the characteristic polynomial of a square matrix. We demonstrate that each coefficient can be efficiently represented by a set of circle graphs. Thus, one can employ…
We briefly describe some well-known means and their properties, focusing on the relationship with integer sequences. In particular, the harmonic numbers, deriving from the harmonic mean, motivate the definition of a new kind of mean that we…
We introduce a class of pairs of graphs consisting of two cliques joined by an arbitrary number of edges. The members of a pair have the property that the clique-bridging edge-set of one graph is the complement of that of the other. We…
A complex harmonic polynomial is the sum of a complex polynomial and a conjugated complex polynomial, of degrees $n$ and $m$ respectively. Li and Wei (2009) presented a formula for the expected number of zeros of a random harmonic…
We study the degrees of homogeneous harmonic maps between simplicial cones. Such maps have been used to model the local behavior of harmonic maps between singular spaces, where the degrees of homogeneous approximations describe the…
We state and prove a general summation identity. The identity is then applied to derive various summation formulas involving the generalized harmonic numbers and related quantities. Interesting results, mostly new, are obtained for both…
Series representations consisting of spherical harmonics are obtained for characteristic exponents and probability density functions of multivariate stable distributions under various conditions. A esult potentially applicable in a…
Graph polynomials are polynomials assigned to graphs. Interestingly, they also arise in many areas outside graph theory as well. Many properties of graph polynomials have been widely studied. In this paper, we survey some results on the…
We interpret the coefficients of the cyclotomic polynomial in terms of simplicial homology.
In this paper, we will show dichotomy theorems for the computation of polynomials corresponding to evaluation of graph homomorphisms in Valiant's model. We are given a fixed graph $H$ and want to find all graphs, from some graph class,…
We investigate a notion of $\times$-homotopy of graph maps that is based on the internal hom associated to the categorical product in the category of graphs. It is shown that graph $\times$-homotopy is characterized by the topological…
As a generalization of orbit-polynomial and distance-regular graphs, we introduce the concept of a quotient-polynomial graph. In these graphs every vertex $u$ induces the same regular partition around $u$, where all vertices of each cell…
We use the symmetric product to describe the resultant scheme and discriminant scheme of polynomials two variables.
Various results ensure the existence of large complete bipartite graphs in properly colored graphs when some condition related to a topological lower bound on the chromatic number is satisfied. We generalize three theorems of this kind,…
The parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among…
Averbouch, Godlin and Makowsky define the edge elimination polynomial of a graph by a recurrence relation with respect to the deletion, contraction and extraction of an edge. It generalizes some well-known graph polynomials such as the…
We present recent advances in harmonic analysis on infinite graphs. Our approach combines combinatorial tools with new results from the theory of unbounded Hermitian operators in Hilbert space, geometry, boundary constructions, and spectral…