Related papers: A new approximation to the geometric-arithmetic in…
Here we initiate a program to study relationships between finite groups and arithmetic-geometric invariants in a systematic way. To do this we first introduce a notion of optimal module for a finite group in the setting of holomorphic mock…
In this paper we establish all extremal graphs with respect to augmented eccentric connectivity index among all (simple connected) graphs, among trees and among trees with perfect matching. For graphs that turn out to be extremal explicit…
Past approaches for statistical shape analysis of objects have focused mainly on objects within the same topological classes, e.g., scalar functions, Euclidean curves, or surfaces, etc. For objects that differ in more complex ways, the…
Due to their capacity to encode rich structural information, labeled graphs are often used for modeling various kinds of objects such as images, molecules, and chemical compounds. If pattern recognition problems such as clustering and…
In geometric analysis, an index theorem relates the difference of the numbers of solutions of two differential equations to the topological structure of the manifold or bundle concerned, sometimes using the heat kernels of two higher-order…
The vertex PI index is a distance--based molecular structure descriptor, that recently found numerous chemical applications. In order to increase diversity of this topological index for bipartite graphs, we introduce weighted version…
The number $\sigma_k(G)$ of induced subgraphs with size $k$ of a graph $G$ was introduced recently as the number of $k$-nearly independent vertex subsets of $G$. Results highlighting similarity and difference in the behaviours of $\sigma_1$…
In this short note we introduce a new metric on certain finite groups. It leads to a class of groups for which the element orders satisfy an interesting inequality. This extends the class CP_2 studied in our previous paper [16].
In this survey I should like to introduce some concepts of algebraic geometry and try to demonstrate the fruitful interaction between algebraic geometry and computer algebra and, more generally, between mathematics and computer science. One…
The concept of the \emph{Gutman index}, denoted $Gut(G)$ was introduced for a connected undirected graph $G$. In this note we apply the concept to the underlying graphs of the family of Jaco graphs, (\emph{directed graphs by definition}),…
Unit disk graphs are intersection graphs of circles of unit radius in the plane. We present simple and provably good heuristics for a number of classical NP-hard optimization problems on unit disk graphs. The problems considered include…
The entropy of a graph was first introduced by Rashevsky \cite{Rashevsky} and Trucco \cite{Trucco} to interpret as the structural information content of the graph and serve as a complexity measure. In this paper, we first state a number of…
In this work we present the notion of greyscale of a graph as a colouring of its vertices that uses colours from the real interval [0,1]. Any greyscale induces another colouring by assigning to each edge the non-negative difference between…
The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…
Convex analysis and Gaussian probability are tightly connected, as mostly evident in the theory of linear regression. Our work introduces an algebraic perspective on such relationship, in the form of a diagrammatic calculus of string…
In this paper, the author introduces the concept of the quasi-geometrically convex and defines a new identity for fractional integrals. By using of this identity, author obtains new estimates on generalization of Hadamard, Ostrowski and…
Geometric aspects play an important role in the construction and analysis of structure-preserving numerical methods for a wide variety of ordinary and partial differential equations. Here we review the development and theory of symplectic…
In this paper, we present a series of techniques to describe General Relativity using Geometric Algebra (GA). We emphasize the physical interpretation of quantities and provide a step-by-step guide for performing calculations. In doing so,…
In this paper extremal values of the difference between several graph invariants related to the metric dimension are studied: mixed metric dimension, edge metric dimension and strong metric dimension. These non-trivial extremal values are…
We introduce the partition function of edge-colored graph homomorphisms, of which the usual partition function of graph homomorphisms is a specialization, and present an efficient algorithm to approximate it in a certain domain. Corollaries…