For a (molecular) graph, the first Zagreb index M1 is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices. It is well known that for connected or disconnected graphs with n vertices and m edges, the inequality M2/m ≥ M1/n does not always hold. Here we show that this relati...

For a (molecular) graph, the first Zagreb index M1 is equal to the sum of squares of the vertex degrees, and the second Zagreb index M2 is equal to the sum of products of degrees of pairs of adjacent vertices. In this paper, we study the Zagreb indices of n-vertex connected graphs with k cut vertices, the upper bound for M1and M2-values of n-vertex connected graphs with k cut vertices are deter...

Kim A. Eagle, MD; Geoffrey S. Ginsburg, MD, PhD; Kiran Musunuru, MD, PhD, MPH; William C. Aird, MD; Robert S. Balaban, PhD; Susan K. Bennett, MD; Roger S. Blumenthal, MD; Shaun R. Coughlin, MD, PhD; Karina W. Davidson, PhD; Edward D. Frohlich, MD; Philip Greenland, MD; Gail P. Jarvik, MD, PhD; Peter Libby, MD; Carl J. Pepine, MD; Jeremy N. Ruskin, MD; Arthur E. Stillman, MD, PhD; Jennifer E. Va...

We study the ultraviolet problem for quantum electrodynamics on a three dimensional torus. We start with the lattice gauge theory on a toroidal lattice and seek to control the singularities as the lattice spacing is taken to zero. This is done by following the flow of a sequence of renormalization group transformations. The analysis is facilitated by splitting the space of gauge fields into int...

Abstract. In this paper, we construct a binary linear code connected with the Kloosterman sum for GL(2, q). Here q is a power of two. Then we obtain a recursive formula generating the power moments 2-dimensional Kloosterman sum, equivalently that generating the even power moments of Kloosterman sum in terms of the frequencies of weights in the code. This is done via Pless power moment identity ...