An Extremal Property of the Hexagonal Lattice

An Extremal Property of Fekete Polynomials

An Extremal Property of Turán Graphs

Let Fn,tr(n) denote the family of all graphs on n vertices and tr(n) edges, where tr(n) is the number of edges in the Turán’s graph Tr(n) – the complete r-partite graph on n vertices with partition sizes as equal as possible. For a graph G and a positive integer λ, let PG(λ) denote the number of proper vertex colorings of G with at most λ colors, and let f(n, tr(n), λ) = max{PG(λ) : G ∈ Fn,tr(n...

An extremal property of Bernstein operators

We establish a strong version of a known extremal property of Bernstein operators, as well as several characterizations of a related specific class of positive polynomial operators. © 2006 Elsevier Inc. All rights reserved. MSC: 41A36; 26D15

The Extremal Graphs for (Sum-) Balaban Index of Spiro and Polyphenyl Hexagonal Chains

As highly discriminant distance-based topological indices, the Balaban index and the sum-Balaban index of a graph $G$ are defined as $J(G)=frac{m}{mu+1}sumlimits_{uvin E} frac{1}{sqrt{D_{G}(u)D_{G}(v)}}$ and $SJ(G)=frac{m}{mu+1}sumlimits_{uvin E} frac{1}{sqrt{D_{G}(u)+D_{G}(v)}}$, respectively, where $D_{G}(u)=sumlimits_{vin V}d(u,v)$ is the distance sum of vertex $u$ in $G$, $m$ is the n...

Transcendental Lattice of an Extremal Elliptic Surface

We develop an algorithm computing the transcendental lattice and the Mordell–Weil group of an extremal elliptic surface. As an example, we compute the lattices of four exponentially large series of surfaces