The vast majority of real-world networks are scalefree, loopy, and sparse, with a power-law degree distribution and a constant average degree. In this paper, we study first-order consensus dynamics in binary scale-free networks, where vertices are subject to white noise. We focus on the coherence of networks characterized in terms of the H2-norm, which quantifies how closely agents track the co...

We introduce recursive corona graphs as a model of small-world networks. We investigate analytically the critical characteristics of the model, including order and size, degree distribution, average path length, clustering coefficient, and the number of spanning trees, as well as Kirchhoff index. Furthermore, we study the spectra for the adjacency matrix and the Laplacian matrix for the model. ...

the reader to [1], [16], [17], [21], and their bibliographies, to get a taste of the variety of approaches used to study this descriptor. In [28], Zhou et al. studied the extremal graphs with given matching number, connectivity and the minimal Kirchhoff index. Also in [23], [25] and [26] the authors determined independently the extremality on the unicyclic graphs with respect to the Kirchhoff i...

We give a shorter proof of a slightly weaker version of a theorem fromGuth and Katz (Ann Math 181:155–190, 2015): we prove that if L is a set of L lines in R3 with at most L1/2 lines in any low degree algebraic surface, then the number of r -rich points of L is L(3/2)+εr−2. This result is one of the main ingredients in the proof of the distinct distance estimate in Guth and Katz (2015). With ou...

Detection of discourse structure is crucial in many text-based applications. This paper presents an original framework for describing textual parallelism which allows us to generalize various discourse phenomena and to propose a unique method to recognize them. With this prospect, we discuss several methods in order to identify the most appropriate one for the problem, and evaluate them based o...

We obtain several formulas for the Euclidean distance degree (ED degree) of an arbitrary nonsingular variety in projective space: in terms of Chern and Segre classes, Milnor classes, Chern-Schwartz-MacPherson classes, and an extremely simple formula equating the Euclidean distance degree of X with the Euler characteristic of an open subset of X.

Inequalities provide a way to study topological indices relatively. There are two major classes of topological indices: degree-based and distance-based indices. In this paper we provide a relative study of these classes and derive inequalities between degree-based indices such as Randić connectivity, GA, ABC, and harmonic indices and distance-based indices such as eccentric connectivity, connec...

Department of Computing and Information Technology, Fudan University, Shanghai, China 2 Theoretical Systems Biology Lab , School of Life Science, Fudan University, Shanghai, China Human Genetics Center, University of Texas Health Science Center at Houston, Houston, TX 77225, USA Abstract In recent years, evaluating graph distance has become more and more important in a variety of real applicati...

*Correspondence: [email protected] Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O. Box 14115-137, Tehran, Iran Abstract In (Hamzeh et al. in Stud. Univ. Babeş-Bolyai, Chem., 4:73-85, 2012), we introduced a generalization of a degree distance of graphs as a new topological index. In this paper, we characterize the n-vertex tricyclic graphs whi...