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...

Reverse addressing is an interesting realization of kinship terms in interactive, face to face communication. This descriptive study was proposed to examine the use of family address pronouns in Iran as a function of the classical sociological parameters of age, sex, and social distance. It investigated various aspects of reverse addressing as a vernacular phenomenon. Data were reported from th...

In this paper characterizations of connected unicyclic and bicyclic graphs in terms of the degree sequence, as well as the graphs in these classes minimal with respect to the degree distance are given. © 2007 Elsevier B.V. All rights reserved.

We address the problem of approximating the distance of sparse graphs from having some predefined property P. The distance of G from having P is εP(G) if the minimum number of edge modifications needed in order to enforce P on G is εP(G) · m̄, where m̄ is an upper bound on the number of edges in the graph. When dealing with bounded-degree graphs of maximal degree d we take m̄ = dn, where n is the ...

We present an algorithm for calculating the quartet distance between two evolutionary trees of bounded degree on a common set of n species. The previous best algorithm has running time O(d2n2) when considering trees, where no node is of more than degree d. The algorithm developed herein has running time O(d9n log n)) which makes it the first algorithm for computing the quartet distance between ...