scholarly journals Spectral Properties with the Difference between Topological Indices in Graphs

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Akbar Jahanbani ◽  
Roslan Hasni ◽  
Zhibin Du ◽  
Seyed Mahmoud Sheikholeslami
Keyword(s):  
Characteristic Polynomial ◽  
Lower Bounds ◽  
Adjacency Matrix ◽  
Spectral Properties ◽  
Main Tool ◽  
Topological Indices ◽  
Upper And Lower Bounds ◽  
New Energy ◽  
Energy Of Graph ◽  
The Difference

Let G be a graph of order n with vertices labeled as v1,v2,…,vn. Let di be the degree of the vertex vi, for i=1,2,…,n. The difference adjacency matrix of G is the square matrix of order n whose i,j entry is equal to di+dj−2−1/didj if the vertices vi and vj of G are adjacent or vivj∈EG and zero otherwise. Since this index is related to the degree of the vertices of the graph, our main tool will be an appropriate matrix, that is, a modification of the classical adjacency matrix involving the degrees of the vertices. In this paper, some properties of its characteristic polynomial are studied. We also investigate the difference energy of a graph. In addition, we establish some upper and lower bounds for this new energy of graph.

Hermitian energy and Hermitian Estrada index of digraphs

2019 ◽  
Vol 13 (06) ◽  
pp. 2050116 ◽  
Author(s):  
Akbar Jahanbani
Keyword(s):  
Lower Bounds ◽  
Adjacency Matrix ◽  
Hermitian Matrix ◽  
Upper And Lower Bounds ◽  
Estrada Index

Let [Formula: see text] be a digraph of order [Formula: see text], and [Formula: see text] be spectrum of the Hermitian adjacency matrix. The main purpose of this paper is to introduce the Hermitian energy and Hermitian Estrada index of a digraph, both based on the eigenvalues of the Hermitian matrix. Moreover, we establish upper and lower bounds for these new digraph invariants, and relations between them.

ON THE DIFFERENCE OF COEFFICIENTS OF OZAKI CLOSE-TO-CONVEX FUNCTIONS

2020 ◽  
pp. 1-8
Author(s):  
YOUNG JAE SIM ◽  
DEREK K. THOMAS
Keyword(s):  
Unit Disk ◽  
Lower Bounds ◽  
Convex Functions ◽  
Univalent Functions ◽  
Upper And Lower Bounds ◽  
The Difference

Let $f$ be analytic in the unit disk $\mathbb{D}=\{z\in \mathbb{C}:|z|<1\}$ and ${\mathcal{S}}$ be the subclass of normalised univalent functions given by $f(z)=z+\sum _{n=2}^{\infty }a_{n}z^{n}$ for $z\in \mathbb{D}$ . We give sharp upper and lower bounds for $|a_{3}|-|a_{2}|$ and other related functionals for the subclass ${\mathcal{F}}_{O}(\unicode[STIX]{x1D706})$ of Ozaki close-to-convex functions.

scholarly journals EXACT UPPER AND LOWER BOUNDS ON THE DIFFERENCE BETWEEN THE ARITHMETIC AND GEOMETRIC MEANS

2015 ◽  
Vol 92 (1) ◽  
pp. 149-158 ◽  
Author(s):  
IOSIF PINELIS
Keyword(s):  
Convex Function ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Jensen Inequality ◽  
Geometric Means ◽  
The Difference

Exact upper and lower bounds on the difference between the arithmetic and geometric means are obtained. The inequalities providing these bounds may be viewed, respectively, as a reverse Jensen inequality and an improvement of the direct Jensen inequality, in the case when the convex function is the exponential.

scholarly journals Dimer–monomer model on the Towers of Hanoi graphs

2015 ◽  
Vol 29 (23) ◽  
pp. 1550173 ◽  
Author(s):  
Hanlin Chen ◽  
Renfang Wu ◽  
Guihua Huang ◽  
Hanyuan Deng
Keyword(s):  
Asymptotic Behavior ◽  
Lower Bounds ◽  
Statistical Physics ◽  
Upper And Lower Bounds ◽  
Recursion Relations ◽  
Sierpiński Graphs ◽  
Towers Of Hanoi ◽  
The Difference ◽  
Significant Figures

The number of dimer–monomers (matchings) of a graph [Formula: see text] is an important graph parameter in statistical physics. Following recent research, we study the asymptotic behavior of the number of dimer–monomers [Formula: see text] on the Towers of Hanoi graphs and another variation of the Sierpiński graphs which is similar to the Towers of Hanoi graphs, and derive the recursion relations for the numbers of dimer–monomers. Upper and lower bounds for the entropy per site, defined as [Formula: see text], where [Formula: see text] is the number of vertices in a graph [Formula: see text], on these Sierpiński graphs are derived in terms of the numbers at a certain stage. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of the entropy can be evaluated with more than a hundred significant figures accuracy.

scholarly journals The Mean Width of Circumscribed Random Polytopes

2010 ◽  
Vol 53 (4) ◽  
pp. 614-628 ◽  
Author(s):  
Károly J. Böröczky ◽  
Rolf Schneider
Keyword(s):  
Convex Body ◽  
Asymptotic Formula ◽  
Uniform Distribution ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Simplicial Polytope ◽  
Mean Width ◽  
The Mean ◽  
The Difference ◽  
Precise Asymptotic

AbstractFor a given convex body K in ℝd, a random polytope K(n) is defined (essentially) as the intersection of n independent closed halfspaces containing K and having an isotropic and (in a specified sense) uniform distribution. We prove upper and lower bounds of optimal orders for the difference of the mean widths of K(n) and K as n tends to infinity. For a simplicial polytope P, a precise asymptotic formula for the difference of the mean widths of P(n) and P is obtained.

scholarly journals Relations between ordinary and multiplicative degree-based topological indices

Filomat ◽  
2018 ◽  
Vol 32 (8) ◽  
pp. 3031-3042 ◽  
Author(s):  
Ivan Gutman ◽  
Igor Milovanovic ◽  
Emina Milovanovic
Keyword(s):  
Lower Bounds ◽  
Connected Graph ◽  
Topological Indices ◽  
Upper And Lower Bounds ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Vertex Degrees ◽  
Simple Connected Graph

Let G be a simple connected graph with n vertices and m edges, and sequence of vertex degrees d1 ? d2 ?...? dn > 0. If vertices i and j are adjacent, we write i ~ j. Denote by ?1, ?*1, Q? and H? the multiplicative Zagreb index, multiplicative sum Zagreb index, general first Zagreb index, and general sumconnectivity index, respectively. These indices are defined as ?1 = ?ni=1 d2i, ?*1 = ?i~j(di+dj), Q? = ?n,i=1 d?i and H? = ?i~j(di+dj)?. We establish upper and lower bounds for the differences H?-m (?1*)?/m and Q?-n(?1)?/2n . In this way we generalize a number of results that were earlier reported in the literature.

scholarly journals On the Difference of Coefficients of Starlike and Convex Functions

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1521
Author(s):  
Young Jae Sim ◽  
Derek K. Thomas
Keyword(s):  
Unit Disk ◽  
Lower Bounds ◽  
Convex Functions ◽  
Univalent Functions ◽  
Starlike Functions ◽  
Upper And Lower Bounds ◽  
Starlike And Convex Functions ◽  
The Difference

Let f be analytic in the unit disk D={z∈C:|z|<1}, and S be the subclass of normalized univalent functions given by f(z)=z+∑n=2∞anzn for z∈D. Let S*⊂S be the subset of starlike functions in D and C⊂S the subset of convex functions in D. We give sharp upper and lower bounds for |a3|−|a2| for some important subclasses of S* and C.

scholarly journals On the Difference of Inverse Coefficients of Univalent Functions

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2040
Author(s):  
Young Jae Sim ◽  
Derek Keith Thomas
Keyword(s):  
Unit Disk ◽  
Lower Bounds ◽  
Upper Bound ◽  
Convex Functions ◽  
Univalent Functions ◽  
Inverse Function ◽  
Starlike Functions ◽  
Upper And Lower Bounds ◽  
The Difference ◽  
Bazilevic Functions

Let f be analytic in the unit disk D={z∈C:|z|<1}, and S be the subclass of normalized univalent functions with f(0)=0, and f′(0)=1. Let F be the inverse function of f, given by F(z)=ω+∑n=2∞Anωn for some |ω|≤r0(f). Let S*⊂S be the subset of starlike functions in D, and C the subset of convex functions in D. We show that −1≤|A3|−|A2|≤3 for f∈S, the upper bound being sharp, and sharp upper and lower bounds for |A3|−|A2| for the more important subclasses of S* and C, and for some related classes of Bazilevič functions.

scholarly journals New Bounds for Topological Indices on Trees through Generalized Methods

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1097 ◽  
Author(s):  
Álvaro Martínez-Pérez ◽  
José M. Rodríguez
Keyword(s):  
Large Class ◽  
Lower Bounds ◽  
Maximum Degree ◽  
Chemical Compounds ◽  
Wiener Index ◽  
Topological Indices ◽  
Upper And Lower Bounds ◽  
Unified Approach ◽  
Wide Family ◽  
New Inequalities

Topological indices are useful for predicting the physicochemical behavior of chemical compounds. A main problem in this topic is finding good bounds for the indices, usually when some parameters of the graph are known. The aim of this paper is to use a unified approach in order to obtain several new inequalities for a wide family of topological indices restricted to trees and to characterize the corresponding extremal trees. The main results give upper and lower bounds for a large class of topological indices on trees, fixing or not the maximum degree. This class includes the first variable Zagreb, the Narumi–Katayama, the modified Narumi–Katayama and the Wiener index.

Estimates of the mean size of the subset image under composition of random mappings

2018 ◽  
Vol 28 (5) ◽  
pp. 331-338 ◽  
Author(s):  
Andrey M. Zubkov ◽  
Aleksandr A. Serov
Keyword(s):  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Random Mappings ◽  
Mean Size ◽  
The Mean ◽  
The Difference ◽  
Time Memory Tradeoff

Abstract Let XN be a set of N elements and F1, F2,… be a sequence of random independent equiprobable mappings XN → N. For a subset S0 ⊂ XN, |S0|=m, we consider a sequence of its images St=Ft(…F2(F1(S0))…), t=1,2… An approach to the exact recurrent computation of distribution of |St| is described. Two-sided inequalities forM{|St|||S0|=m} such that the difference between the upper and lower bounds is o(m)for m, t, N → ∞, mt=o(N) are derived. The results are of interest for the analysis of time-memory tradeoff algorithms.

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