相关论文: Computing the Wiener index in Sierpinski carpet gr…
The relation between the Wiener index $W(G)$ and the eccentricity $\varepsilon(G)$ of a graph $G$ is studied. Lower and upper bounds on $W(G)$ in terms of $\varepsilon(G)$ are proved and extremal graphs characterized. A Nordhaus-Gaddum type…
The correct computation of orbits of discrete dynamical systems on the interval is considered. Therefore, an arbitrary-precision floating-point approach based on automatic error analysis is chosen and a general algorithm is presented. The…
We give an efficient algorithm to compute equations of twists of hyperelliptic curves of arbitrary genus over any separable field (of characteristic different from 2), and we explicitly describe some interesting examples.
For a connected graph $G$, the Wiener index, denoted by $W(G)$, is the sum of the distance of all pairs of distinct vertices and the eccentricity, denoted by $\varepsilon(G)$, is the sum of the eccentricity of individual vertices. In…
In this article we present recent advances on interval methods for rigorous computation of Poincar\'e maps. We also discuss the impact of choice of Poincar\'e section and coordinate system on obtained bounds for computing Poincar\'e map…
The Hosoya polynomial of a graph encompasses many of its metric properties, for instance the Wiener index (alias average distance) and the hyper-Wiener index. An expression is obtained that reduces the computation of the Hosoya polynomials…
The universal Gr\"obner basis of an ideal is a Gr\"obner basis with respect to all term orders simultaneously. The aim of this paper is to present an algorithmic approach to compute the universal Gr\"obner basis for the toric ideal…
This paper completes the project started in [10]; to solve the edge-isoperimetric problem on the (generalized and extended) Sierpinski graph, S(n,m). We prove that initial segments of lexicographic order are solutions of the EIP for all…
We estimate the distance in the curve graph of a surface S of finite type using Teichmueller geodesics and assuming to be able to detect curves of distance at least three.
We consider weighted tiling systems to represent functions from graphs to a commutative semiring such as the Natural semiring or the Tropical semiring. The system labels the nodes of a graph by its states, and checks if the neighbourhood of…
The concept of geometric-arithmetic index was introduced in the chemical graph theory recently, but it has shown to be useful. The aim of this paper is to obtain new inequalities involving the geometric-arithmetic index $GA_1$ and…
In many applications that involve the inference of an unknown smooth function, the inference of its derivatives will often be just as important as that of the function itself. To make joint inferences of the function and its derivatives, a…
For Paley-Wiener functions on weighted combinatorial finite or infinite graphs we develop a weighted sampling theory in which samples are defined as inner products with weight functions (measuring devices). Three reconstruction methods are…
Algorithms for the fast and exact computation of Wigner matrices are described and their application to a fast and massively parallel 4pi convolution code between a beam and a sky is also presented.
We consider a new Steiner tree problem, called vertex-cover-weighted Steiner tree problem. This problem defines the weight of a Steiner tree as the minimum weight of vertex covers in the tree, and seeks a minimum-weight Steiner tree in a…
A simple and efficient algorithm to numerically compute the genus of surfaces of three-dimensional objects using the Euler characteristic formula is presented. The algorithm applies to objects obtained by thresholding a scalar field in a…
The exact computation of orbits of discrete dynamical systems on the interval is considered. Therefore, a multiple-precision floating point approach based on error analysis is chosen and a general algorithm is presented. The correctness of…
A visibility algorithm maps time series into complex networks following a simple criterion. The resulting visibility graph has recently proven to be a powerful tool for time series analysis. However its straightforward computation is…
We introduce the regularized integrals for decorated graphs on elliptic curves, which produces an almost holomorphic function on upper half plane. Then we give the graph version of holomorphic anomaly equation to study the anti-holomorphic…
Wattenhofer [WW04] derive a complicated distributed algorithm to compute a weighted matching of an arbitrary weighted graph, that is at most a factor 5 away from the maximum weighted matching of that graph. We show that a variant of the…