If G is a connected graph with vertex set V (G), then the degree distance of G is defined as DD(G) = ∑ {u,v}∈V (G)(deg u + deg v)d(u, v), where deg u is the degree of vertex u, and d(u, v) denotes the distance between u and v. In the chemical literature, DD(G) is better known under ‡Corresponding author. If possible, send your correspondence via e-mail. the name Schultz index. In the class of p...

We present two algorithms for computing the quartet distance between trees of arbitrary degree. The quartet distance between two unrooted evolutionary trees is the number of quartets—sub-trees induced by four leaves—that differs between the trees. Previous algorithms focus on computing the quartet distance between binary trees. In this paper, we present two algorithms for computing the quartet ...

In this paper, we present the various upper and lower bounds for the product version of reciprocal degree distance in terms of other graph inavriants. Finally, we obtain the upper bounds for the product version of reciprocal degree distance of the composition, Cartesian product and double of a graph in terms of other graph invariants including the Harary index and Zagreb indices. .

The nearest point map of a real algebraic variety with respect to Euclidean distance is an algebraic function. For instance, for varieties of low rank matrices, the Eckart-Young Theorem states that this map is given by the singular value decomposition. This article develops a theory of such nearest point maps from the perspective of computational algebraic geometry. The Euclidean distance degre...

We show that the Euclidean distance degree of a real orthogonally invariant matrix variety equals the Euclidean distance degree of its restriction to diagonal matrices. We illustrate how this result can greatly simplify calculations in concrete circumstances.

Let G be a graph with vertex set V(G) and edge set E(G). For any two vertices x and y in V(G), the distance between x and y, denoted by d(x,y), is the length of the shortest path connecting x and y. The degree of a vertex v in G is the number of neighbors of v in G. Numbers reflecting certain structural features of organic molecules that are obtained from the molecular graph are usually called ...

Abstract. Distance energy is a newly introduced molecular graph-based analog of the total π-electron energy, and it is defined as the sum of the absolute eigenvalues of the molecular distance matrix. For trees and unicyclic graphs, distance energy is equal to the doubled value of the distance spectral radius. In this paper, we introduce a general transformation that increases the distance spect...

Although initial interest in science, technology, engineering and mathematics (STEM) is high, recruitment and retention remains a challenge, and some populations are disproportionately underrepresented in STEM fields. To address these challenges, the Microbiology and Cell Science Department in the College of Agricultural and Life Sciences at the University of Florida has developed an innovative...

We show that it is possible to route locally and competitively on two bounded-degree plane 6-spanners, one with maximum degree 12 and the other with maximum degree 9. Both spanners are subgraphs of the empty equilateral triangle Delaunay triangulation. First, in a weak routing model where the only information stored at each vertex is its neighbourhood, we show how to find a path between any two...

We study the propagation of gravitons within 5-D supersymmetric braneworld models with a bulk scalar field. The setup considered here consists of a 5-D bulk spacetime bounded by two 4-D branes localized at the fixed points of an S/Z2 orbifold. There is a scalar field φ in the bulk which, provided a superpotential W (φ), determines the warped geometry of the 5-D spacetime. This type of scenario ...