Related papers: A new approximation to the geometric-arithmetic in…
The aim of this paper is to obtain new sharp inequalities for a large family of topological indices, including the first variable Zagreb index $M_1^\alpha$, and to characterize the set of extremal graphs with respect to them. Our main…
This survey concerns regular graphs that are extremal with respect to the number of independent sets, and more generally, graph homomorphisms. More precisely, in the family of of $d$-regular graphs, which graph $G$ maximizes/minimizes the…
The geometric--arithmetic indices are widely considered in the chemical graph theory in the last decade. The reason of introducing new indices is to gain prediction of target properties of considered molecules that is better than the…
Let $G$ be a molecular graph. The total-eccentricity index of graph $G$ is defined as the sum of eccentricities of all vertices of $G$. %In [R. Farooq, M.A. Malik, J. Rada, Extremal graphs with respect to total-eccentricity index, 2017,…
We survey various aspects of infinite extremal graph theory and prove several new results. The lead role play the parameters connectivity and degree. This includes the end degree. Many open problems are suggested.
Topological indices are graph-theoretic descriptors that play a crucial role in mathematical chemistry, capturing the structural characteristics of molecules and enabling the prediction of their physicochemical properties. A widely studied…
A geometric graph is a combinatorial graph, endowed with a geometry that is inherited from its embedding in a Euclidean space. Formulation of a meaningful measure of (dis-)similarity in both the combinatorial and geometric structures of two…
Some years ago, the harmonic polynomial was introduced in order to understand better the harmonic topological index; for instance, it allows to obtain bounds of the harmonic index of the main products of graphs. Here, we obtain several…
In this paper we introduced an arithmetic graph function which associates with every group G the directed graph whose vertices corresponds to the divisors of |G|. With the help of such functions we introduced arithmetic graphs of classes of…
A geometric setup for constrained variational calculus is presented. The analysis deals with the study of the extremals of an action functional defined on piecewise differentiable curves, subject to differentiable, non-holonomic…
We survey recent advances in the theory of graph and hypergraph decompositions, with a focus on extremal results involving minimum degree conditions. We also collect a number of intriguing open problems, and formulate new ones.
Paper is devoted to extremal problems in geometric function theory of complex variables associated with estimates of functionals defined on the systems of non-overlapping domains. In particular, we strengthen some known result in this…
A geometric representation for multivariate extremes, based on the shapes of scaled sample clouds in light-tailed margins and their so-called limit sets, has recently been shown to connect several existing extremal dependence concepts.…
Computers and algorithms play an ever-increasing role in obtaining new results in graph theory. In this survey, we present a broad range of techniques used in computer-assisted graph theory, including the exhaustive generation of all…
The question on connection between the structure of a finite group $G$ and the properties of the indices of elements of $G$ has been a popular research topic for many years. The $p$-index $|x^G|_p$ of an element $x$ of a group $G$ is the…
A recent development in extreme value modeling uses the geometry of the dataset to perform inference on the multivariate tail. A key quantity in this inference is the gauge function, whose values define this geometry. Methodology proposed…
The pseudoachromatic index of a graph is the maximum number of colors that can be assigned to its edges, such that each pair of different colors is incident to a common vertex. If for each vertex its incident edges have different color,…
We propose a new graph-theoretic benchmark in this paper. The benchmark is developed to address shortcomings of an existing widely-used graph benchmark. We thoroughly studied a large number of traditional and contemporary graph algorithms…
Recently, a couple of degree-based topological indices, defined using a geometrical point of view of a graph edge, have attracted significant attention and being extensively investigated. Furtula and Oz [Complementary Topological Indices,…
Recently there has been increased interest in fitting generative graph models to real-world networks. In particular, Bl\"asius et al. have proposed a framework for systematic evaluation of the expressivity of random graph models. We extend…