Related papers: A new approximation to the geometric-arithmetic in…
In this article, the author proposes a new approach for the estimating of the number of edges in induced subgraphs of a special distance graph. Author significantly improves previous estimates and suggests a new approach to obtaining better…
We give inequalities relating the eigenvalues of the adjacency matrix and the Laplacian of a graph, and its minimum and maximum degrees. The results are applied to derive new conditions for quasi-randomness of graphs.
In this paper, we define the quotinet graphs. In particular, we introduce the boundary quotient graphs, admissible boundary quotient graphs and subgraph boundary qoutient graphs. By the property of the quotient spaces, the boundary…
In this paper we are concerned with various graph invariants (girth, diameter, expansion constants, eigenvalues of the Laplacian, tree number) and their analogs for weighted graphs -- weighing the graph changes a combinatorial problem to…
Active contour models based on partial differential equations have proved successful in image segmentation, yet the study of their geometric formulation on arbitrary geometric graphs is still at an early stage. In this paper, we introduce…
In this paper, we introduce the notion of relative ultragraph algebras and extend classical injectivity criteria for representations, particularly those arising from branching systems,to this relative setting. This new concept is closely…
Comparison of geometric quantities usually means obtaining generally true equalities of different algebraic expressions of a given geometric figure. Today's technical possibilities already support symbolic proofs of a conjectured theorem,…
Many scientific problems require to process data in the form of geometric graphs. Unlike generic graph data, geometric graphs exhibit symmetries of translations, rotations, and/or reflections. Researchers have leveraged such inductive bias…
A graph $G$ is defined encapsulating the number theoretic notion of the Fundamental Theorem of Arithmetic. We then provide a graph theoretic approach to the fundamental results on the coprimality of two natural numbers, through the use of…
We introduce the first geometric construction of codes in the sum-rank metric, which we called linearized Algebraic Geometry codes, using quotients of the ring of Ore polynomials with coefficients in the function field of an algebraic…
We investigate the arithmetic-harmonic inequality (AHI) index, a bounded and scale-invariant measure of dispersion for positive random variables, defined through the interplay between the mean and its reciprocal. We derive analytical…
A novel approach to complex problems has been previously applied to graph classification and the graph equivalence problem. Here we consider its applications to a wide set of NP complete problems, namely, those of finding a subgraph g…
Introduced the quantitative measure of the structural complexity of the graph (complex network, etc.) based on a procedure similar to the renormalization process, considering the difference between actual and averaged graph structures on…
Many real-world networks of interest are embedded in physical space. We present a new random graph model aiming to reflect the interplay between the geometries of the graph and of the underlying space. The model favors configurations with…
A survey on recent developments in (algebraic) integral geometry is given. The main focus lies on algebraic structures on the space of translation invariant valuations and applications in integral geometry.
Extremal Graph Theory is a very deep and wide area of modern combinatorics. It is very fast developing, and in this long but relatively short survey we select some of those results which either we feel very important in this field or which…
We shall give a refinement of the arithmetic-geometric mean inequality.
Recently, Ali et al. posed several open problems concerning extremal graphs with respect to the ABS index. These problems involve characterizing graphs that attain the maximum ABS index within specific graph classes, including: connected…
In the branch of mathematics known as graph theory, graphs are considered as a set of points, called vertices, with connections between these points, called edges. The purpose of this paper is to study mappings between two graphs that have…
This paper is devoted to a systematic study of certain geometric integral inequalities which arise in continuum combinatorial approaches to $L^p$-improving inequalities for Radon-like transforms over polynomial submanifolds of intermediate…