Distance-based indices of complete m-ary trees

2020 ◽  
Vol 12 (04) ◽  
pp. 2050041
Author(s):  
Mesfin Masre ◽  
Samuel Asefa Fufa ◽  
Tomáš Vetrík
Keyword(s):  
Computer Science ◽  
Recurrence Relations ◽  
Wiener Index ◽  
The Other ◽  
Binary Trees ◽  
New Methods ◽  
Degree Distance ◽  
Gutman Index ◽  
Eccentric Distance

Binary and [Formula: see text]-ary trees have extensive applications, particularly in computer science and chemistry. We present exact values of all important distance-based indices for complete [Formula: see text]-ary trees. We solve recurrence relations to obtain the value of the most well-known index called the Wiener index. New methods are used to express the other indices (the degree distance, the eccentric distance sum, the Gutman index, the edge-Wiener index, the hyper-Wiener index and the edge-hyper-Wiener index) as well. Values of distance-based indices for complete binary trees are corollaries of the main results.

scholarly journals WIENER INDEX OF TREES OF GIVEN ORDER AND DIAMETER AT MOST

2013 ◽  
Vol 89 (3) ◽  
pp. 379-396 ◽  
Author(s):  
SIMON MUKWEMBI ◽  
TOMÁŠ VETRÍK
Keyword(s):  
Upper Bound ◽  
Open Problem ◽  
Wiener Index ◽  
Upper Bounds ◽  
Degree Distance ◽  
Gutman Index

AbstractThe long-standing open problem of finding an upper bound for the Wiener index of a graph in terms of its order and diameter is addressed. Sharp upper bounds are presented for the Wiener index, and the related degree distance and Gutman index, for trees of order$n$and diameter at most$6$.

Further results on Zagreb eccentricity coindices

2020 ◽  
Vol 12 (06) ◽  
pp. 2050075
Author(s):  
Mahdieh Azari
Keyword(s):  
Wiener Index ◽  
Connectivity Index ◽  
Lower And Upper Bounds ◽  
Graph Invariants ◽  
Eccentric Connectivity Index ◽  
Size Number ◽  
Connectivity Indices ◽  
Degree Distance ◽  
Graph Parameters ◽  
Eccentric Distance

The eccentric connectivity index and second Zagreb eccentricity index are well-known graph invariants defined as the sums of contributions dependent on the eccentricities of adjacent vertices over all edges of a connected graph. The coindices of these invariants have recently been proposed by considering analogous contributions from the pairs of non-adjacent vertices. Here, we obtain several lower and upper bounds on the eccentric connectivity coindex and second Zagreb eccentricity coindex in terms of some graph parameters such as order, size, number of non-adjacent vertex pairs, radius, and diameter, and relate these invariants to some well-known graph invariants such as Zagreb indices and coindices, status connectivity indices and coindices, ordinary and multiplicative Zagreb eccentricity indices, Wiener index, degree distance, total eccentricity, eccentric connectivity index, second eccentric connectivity index, and eccentric-distance sum. Moreover, we compute the values of these coindices for two graph constructions, namely, double graphs and extended double graphs.

scholarly journals Remarks on Distance Based Topological Indices for ℓ-Apex Trees

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 802
Author(s):  
Martin Knor ◽  
Muhammad Imran ◽  
Muhammad Kamran Jamil ◽  
Riste Škrekovski
Keyword(s):  
Graph Theory ◽  
Wiener Index ◽  
Extreme Value ◽  
Topological Indices ◽  
The Other ◽  
Harary Index ◽  
Open Questions ◽  
Degree Distance ◽  
The One ◽  
Extremal Values

A graph G is called an ℓ-apex tree if there exist a vertex subset A ⊂ V ( G ) with cardinality ℓ such that G − A is a tree and there is no other subset of smaller cardinality with this property. In the paper, we investigate extremal values of several monotonic distance-based topological indices for this class of graphs, namely generalized Wiener index, and consequently for the Wiener index and the Harary index, and also for some newer indices as connective eccentricity index, generalized degree distance, and others. For the one extreme value we obtain that the extremal graph is a join of a tree and a clique. Regarding the other extreme value, which turns out to be a harder problem, we obtain results for ℓ = 1 and pose some open questions for higher ℓ. Symmetry has always played an important role in Graph Theory, in recent years, this role has increased significantly in several branches of this field, including topological indices of graphs.

scholarly journals Error Analysis for a Noisy Lacunary Cubic Spline Interpolation and a Simple Noisy Cubic Spline Quasi Interpolation

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Feng-Gong Lang ◽  
Xiao-Ping Xu
Keyword(s):  
Error Analysis ◽  
Error Bounds ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Cubic Spline ◽  
The Other ◽  
Cubic Spline Interpolation ◽  
Numerical Tests ◽  
New Methods ◽  
Noisy Function

We mainly present the error analysis for two new cubic spline based methods; one is a lacunary interpolation method and the other is a very simple quasi interpolation method. The new methods are able to reconstruct a function and its first two derivatives from noisy function data. The explicit error bounds for the methods are given and proved. Numerical tests and comparisons are performed. Numerical results verify the efficiency of our methods.

Interaction with geospatial data

2015 ◽  
Vol 57 (1) ◽  
Author(s):  
Johannes Schöning
Keyword(s):  
Human Computer Interaction ◽  
Computer Science ◽  
User Interfaces ◽  
Spatial Information ◽  
Social Computing ◽  
Geospatial Data ◽  
Research Interest ◽  
Research Topics ◽  
Natural User Interfaces ◽  
New Methods

AbstractMy research interest lies at the interaction between human-computer interaction (HCI) and geoinformatics. I am interested in developing new methods and novel user interfaces to navigate through spatial information. This article will give a brief overview on my past and current research topics and streams. Generally speaking, geography is playing an increasingly important role in computer science and also in the field of HCI ranging from social computing to natural user interfaces (NUIs). At the same time, research in geography has focused more and more on technology-mediated interaction with spatiotemporal phenomena. By bridging the two fields, my aim is to exploit this fruitful intersection between those two and develop, design and evaluate user interfaces that help people to solve their daily tasks more enjoyable and effectively.

Gender and National Differences in Attitudes toward Same-Gender Touch

1994 ◽  
Vol 78 (3) ◽  
pp. 1027-1034 ◽  
Author(s):  
Frank N. Willis ◽  
Vicki A. Rawdon
Keyword(s):  
Cultural Differences ◽  
Female Students ◽  
Cross Cultural ◽  
The Other ◽  
Male And Female ◽  
New Methods ◽  
Cross Cultural Differences ◽  
National Differences ◽  
The Us ◽  
Same Gender

Women have been reported to be more positive about same-gender touch, but cross-cultural information about this touch is limited. Male and female students from Chile (n = 26), Spain (n = 61), Malaysia (n = 32), and the US (n = 77) completed a same-gender touch scale. As in past studies, US women had more positive scores than US men. Malaysians had more negative scores than the other three groups. Spanish and US students had more positive scores than Chilean students. National differences in attitudes toward particular types of touch were also noted. The need for new methods for examining cross-cultural differences in touch was discussed.

scholarly journals Meta-Fibonacci Sequences, Binary Trees and Extremal Compact Codes

10.37236/1052 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Brad Jackson ◽  
Frank Ruskey
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Binary Trees ◽  
Integer Sequences ◽  
Number Of Leaves ◽  
Online Encyclopedia ◽  
Fibonacci Sequences ◽  
Infinite Sequences

We consider a family of meta-Fibonacci sequences which arise in studying the number of leaves at the largest level in certain infinite sequences of binary trees, restricted compositions of an integer, and binary compact codes. For this family of meta-Fibonacci sequences and two families of related sequences we derive ordinary generating functions and recurrence relations. Included in these families of sequences are several well-known sequences in the Online Encyclopedia of Integer Sequences (OEIS).

scholarly journals BIOLOGICAL CONTROL IN LEAF-CUTTING ANTS, Atta sexdens (HYMENOPTERA: FORMICIDAE), USING PATHOGENIC FUNGI

2021 ◽  
Vol 45 ◽  
Author(s):  
Tarcísio Marcos Macedo Mota Filho ◽  
Luis Eduardo Pontes Stefanelli ◽  
Roberto da Silva Camargo ◽  
Carlos Alberto Oliveira de Matos ◽  
Luiz Carlos Forti
Keyword(s):  
Biological Control ◽  
Chemical Control ◽  
Pathogenic Fungi ◽  
Behavioral Changes ◽  
The Other ◽  
Fungus Garden ◽  
Atta Sexdens ◽  
Main Method ◽  
New Methods ◽  
Leaf Cutting

ABSTRACT Chemical control using toxic baits containing the active ingredient sulfluramid at 0.3% (w/w) is the main method for controlling leaf-cutting ants of the genera Atta and Acromyrmex. However, since 2009, when sulfluramid was included in Annex B of the Stockholm Convention on Persistent Organic Pollutants, there has been an intense search for new methods that are efficient in controlling these insects. Among said new methods, biological control using pathogenic fungi has shown promising results in laboratory conditions. The objective of this study, given the context presented, was to assess the potential of the fungi Beauveria bassiana and Trichoderma harzianum in controlling Atta sexdens. Colonies of A. sexdens were exposed to the fungi by means of formulated baits provided in a foraging chamber, or of suspensions sprayed on the fungus garden, and had their behavioral changes recorded for 21 days. For both formulations, concentrations of 10 and 20% (w/w) of the fungi being studied were used. The results allowed concluding that baits containing 10 and 20% (w/w) of the fungi B. bassiana and T. harzianum were not efficient in controlling colonies of A sexdens. On the other hand, spraying suspensions of 20% (w/w) of B. bassiana and 10% and 20% (w/w) of T. harzianum was efficient and resulted in 100% mortality of the colonies 11, 9 and 7 days after application, respectively. These findings indicate that the fungi B. bassiana and T. harzianum are promising as agents for the control of A. sexdens colonies, when sprayed on the fungus garden, although there are still some challenges as to their use related to the development of technologies for the application of the pathogen.

scholarly journals The Computational Strength of Extensions of Weak König’s Lemma

1998 ◽  
Vol 5 (41) ◽  
Author(s):  
Ulrich Kohlenbach
Keyword(s):  
Natural Number ◽  
Arbitrary Function ◽  
The Other ◽  
Binary Trees ◽  
Subsequent Paper ◽  
Bounded Functions ◽  
The One ◽  
Weak König’S Lemma ◽  
König’S Lemma

The weak König's lemma WKL is of crucial significance in the study of fragments of mathematics which on the one hand are mathematically strong but on the other hand have a low proof-theoretic and computational strength. In addition to the restriction to binary trees (or equivalently bounded trees), WKL<br />is also `weak' in that the tree predicate is quantifier-free. Whereas in general the computational and proof-theoretic strength increases when logically more complex trees are allowed, we show that this is not the case for trees which are<br />given by formulas in a class Phi where we allow an arbitrary function quantifier prefix over bounded functions in front of a Pi^0_1-formula. This results in a schema Phi-WKL.<br />Another way of looking at WKL is via its equivalence to the principle<br /> For all x there exists y<=1 for all z A0(x; y; z) -> there exists f <= lambda x.1 for all x, z A0(x, fx, z);<br />where A0 is a quantifier-free formula (x, y, z are natural number variables). <br /> We generalize this to Phi-formulas as well and allow function quantifiers `there exists g <= s'<br />instead of `there exists y <= 1', where g <= s is defined pointwise. The resulting schema is called Phi-b-AC^0,1.<br />In the absence of functional parameters (so in particular in a second order context), the corresponding versions of Phi-WKL and Phi-b-AC^0,1 turn out to<br />be equivalent to WKL. This changes completely in the presence of functional<br />variables of type 2 where we get proper hierarchies of principles Phi_n-WKL and<br />Phi_n-b-AC^0,1. Variables of type 2 however are necessary for a direct representation<br />of analytical objects and - sometimes - for a faithful representation of<br />such objects at all as we will show in a subsequent paper. By a reduction of<br />Phi-WKL and Phi-b-AC^0,1 to a non-standard axiom F (introduced in a previous paper) and a new elimination result for F relative to various fragment of arithmetic in all finite types, we prove that Phi-WKL and Phi-b-AC^0,1 do<br />neither contribute to the provably recursive functionals of these fragments nor to their proof-theoretic strength. In a subsequent paper we will illustrate the greater mathematical strength of these principles (compared to WKL).

scholarly journals Distinct partitions and overpartitions

2021 ◽  
Vol 38 (1) ◽  
pp. 149-158
Author(s):  
MIRCEA MERCA ◽  
Keyword(s):  
Partition Function ◽  
Recurrence Relation ◽  
Recurrence Relations ◽  
Convergent Series ◽  
The Other ◽  
Large Integer ◽  
Linear Recurrence ◽  
Fast Computation ◽  
Real Numbers ◽  
Very High

In 1963, Peter Hagis, Jr. provided a Hardy-Ramanujan-Rademacher-type convergent series that can be used to compute an isolated value of the partition function $Q(n)$ which counts partitions of $n$ into distinct parts. Computing $Q(n)$ by this method requires arithmetic with very high-precision approximate real numbers and it is complicated. In this paper, we investigate new connections between partitions into distinct parts and overpartitions and obtain a surprising recurrence relation for the number of partitions of $n$ into distinct parts. By particularization of this relation, we derive two different linear recurrence relations for the partition function $Q(n)$. One of them involves the thrice square numbers and the other involves the generalized octagonal numbers. The recurrence relation involving the thrice square numbers provide a simple and fast computation of the value of $Q(n)$. This method uses only (large) integer arithmetic and it is simpler to program. Infinite families of linear inequalities involving partitions into distinct parts and overpartitions are introduced in this context.

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