scholarly journals Infinitely many equivalent versions of the graceful tree conjecture

2015 ◽  
Vol 9 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Tao-Ming Wang ◽  
Cheng-Chang Yang ◽  
Lih-Hsing Hsu ◽  
Eddie Cheng
Keyword(s):  
Perfect Matching ◽  
Absolute Difference ◽  
Extra Condition ◽  
Graceful Labeling ◽  
The Absolute

A graceful labeling of a graph with q edges is a labeling of its vertices using the integers in [0, q], such that no two vertices are assigned the same label and each edge is uniquely identified by the absolute difference between the labels of its endpoints. The well known Graceful Tree Conjecture (GTC) states that all trees are graceful, and it remains open. It was proved in 1999 by Broersma and Hoede that there is an equivalent conjecture for GTC stating that all trees containing a perfect matching are strongly graceful (graceful with an extra condition). In this paper we extend the above result by showing that there exist infinitely many equivalent versions of the GTC. Moreover we verify these infinitely many equivalent conjectures of GTC for trees of diameter at most 7. Among others we are also able to identify new graceful trees and in particular generalize the ?-construction of Stanton-Zarnke (and later Koh- Rogers-Tan) for building graceful trees through two smaller given graceful trees.

scholarly journals On the Graceful Game

2020 ◽  
Vol 18 (3) ◽  
Author(s):  
Atilio Luiz ◽  
Simone Dantas ◽  
Luisa Ricardo
Keyword(s):  
Connected Graph ◽  
Bipartite Graphs ◽  
Absolute Difference ◽  
Complete Graphs ◽  
Graceful Labeling ◽  
Graph Games ◽  
First Results ◽  
Winning Strategies ◽  
Complete Bipartite Graphs ◽  
The Absolute

A graceful labeling of a graph G with m edges consists in labeling the vertices of G with distinct integers from 0 to m such that, when each edge is assigned the absolute difference of the labels of its endpoints, all induced edge labels are distinct. Rosa established two well known conjectures: all trees are graceful (1966) and all triangular cacti are graceful (1988). In order to contribute to both conjectures we study these problems in the context of graph games. The graceful game was introduced by Tuza in 2017 as a two-players game on a connected graph in which the players Alice and Bob take turns labeling the vertices with distinct integers from 0 to m. Alice’s goal is to gracefully label the graph as Bob’s goal is to prevent it from happening. In this work, we present the first results in this area by showing winning strategies for Alice and Bob in complete graphs, paths, cycles, complete bipartite graphs, caterpillars, prisms, wheels, helms, webs, gear graphs, hypercubes and some powers of paths.

A Metaheuristic Approach to the Graceful Labeling Problem

2010 ◽  
Vol 1 (4) ◽  
pp. 42-56 ◽  
Author(s):  
Houra Mahmoudzadeh ◽  
Kourosh Eshghi
Keyword(s):  
Graph Theory ◽  
Ant Colony Optimization ◽  
Optimization Problem ◽  
Ant Colony ◽  
Absolute Difference ◽  
Graceful Labeling ◽  
The Absolute

In graph theory, a graceful labeling of a graph G = (V, E) with n vertices and m edges is a labeling of its vertices with distinct integers between 0 and m inclusive, such that each edge is uniquely identified by the absolute difference between its endpoints. In this paper, the well-known graceful labeling problem of graphs is represented as an optimization problem, and an algorithm based on Ant Colony Optimization metaheuristic is proposed for finding its solutions. In this regard, the proposed algorithm is applied to different classes of graphs and the results are compared with the few existing methods inside of different literature.

A Metaheuristic Approach to the Graceful Labeling Problem

2012 ◽  
pp. 217-232
Author(s):  
Houra Mahmoudzadeh ◽  
Kourosh Eshghi
Keyword(s):  
Graph Theory ◽  
Ant Colony Optimization ◽  
Optimization Problem ◽  
Ant Colony ◽  
Absolute Difference ◽  
Graceful Labeling ◽  
The Absolute

In graph theory, a graceful labeling of a graph G = (V, E) with n vertices and m edges is a labeling of its vertices with distinct integers between 0 and m inclusive, such that each edge is uniquely identified by the absolute difference between its endpoints. In this paper, the well-known graceful labeling problem of graphs is represented as an optimization problem, and an algorithm based on Ant Colony Optimization metaheuristic is proposed for finding its solutions. In this regard, the proposed algorithm is applied to different classes of graphs and the results are compared with the few existing methods inside of different literature.

scholarly journals Inadequacy of 3-month Oswestry Disability Index outcome for assessing individual longer-term patient experience after lumbar spine surgery

2016 ◽  
Vol 25 (2) ◽  
pp. 170-180 ◽  
Author(s):  
Anthony L. Asher ◽  
Silky Chotai ◽  
Clinton J. Devin ◽  
Theodore Speroff ◽  
Frank E. Harrell ◽  
...  
Keyword(s):  
Patient Experience ◽  
Spine Surgery ◽  
Oswestry Disability Index ◽  
Absolute Difference ◽  
Lumbar Spine Surgery ◽  
Substantial Clinical Benefit ◽  
Degenerative Lumbar Disease ◽  
Spine Care ◽  
The Absolute ◽  
Prospective Longitudinal

OBJECTIVE Prospective longitudinal outcomes registries are at the center of evidence-driven health care reform. Obtaining real-world outcomes data at 12 months can be costly and challenging. In the present study, the authors analyzed whether 3-month outcome measurements sufficiently represent 12-month outcomes for patients with degenerative lumbar disease undergoing surgery. METHODS Data from 3073 patients undergoing elective spine surgery for degenerative lumbar disease were entered into a prospective multicenter registry (N2QOD). Baseline, 3-month, and 12-month follow-up Oswestry Disability Index (ODI) scores were recorded. The absolute differences between actual 12- and 3-month ODI scores was evaluated. Additionally, the authors analyzed the absolute difference between actual 12-month ODI scores and a model-predicted 12-month ODI score (the model used patients' baseline characteristics and actual 3-month scores). The minimal clinically important difference (MCID) for ODI of 12.8 points and the substantial clinical benefit (SCB) for ODI of 18.8 points were used based on the previously published values. The concordance rate of achieving MCID and SCB for ODI at 3-and 12-months was computed. RESULTS The 3-month ODI scores differed from 12-month scores by an absolute difference of 11.9 ± 10.8, and predictive modeling estimations of 12-month ODI scores differed from actual 12-month scores by a mean (± SD) of 10.7 ± 9.0 points (p = 0.001). Sixty-four percent of patients (n = 1982) achieved an MCID for ODI at 3 months in comparison with 67% of patients (n = 2088) by 12 months; 51% (n = 1731) and 61% (n = 1860) of patients achieved SCB for ODI at 3 months and 12 months, respectively. Almost 20% of patients had ODI scores that varied at least 20 points (the point span of an ODI functional category) between actual 3- and 12-month values. In the aggregate analysis of achieving MCID, 77% of patients were concordant and 23% were discordant in achieving or not achieving MCID at 3 and 12 months. The discordance rates of achieving or not achieving MCID for ODI were in the range of 19% to 27% for all diagnoses and treatments (decompression with and without fusion). The positive and negative predictive value of 3-months ODI to predict 12-month ODI was 86% and 60% for MCID and 82% and 67% for SCB. CONCLUSIONS Based on their findings, the authors conclude the following: 1) Predictive methods for functional outcome based on early patient experience (i.e., baseline and/or 3-month data) should be used to help evaluate the effectiveness of procedures in patient populations, rather than serving as a proxy for long-term individual patient experience. 2) Prospective longitudinal registries need to span at least 12 months to determine the effectiveness of spine care at the individual patient and practitioner level.

scholarly journals Comparison of MODIS and AERONET derived aerosol optical depth over the Ganga Basin, India

2005 ◽  
Vol 23 (4) ◽  
pp. 1093-1101 ◽  
Author(s):  
S. N. Tripathi ◽  
Sagnik Dey ◽  
A. Chandel ◽  
S. Srivastava ◽  
Ramesh P. Singh ◽  
...  
Keyword(s):  
Aerosol Optical Depth ◽  
Optical Depth ◽  
Time Window ◽  
Absolute Error ◽  
Absolute Difference ◽  
Ganga Basin ◽  
Monsoon Period ◽  
Post Monsoon ◽  
Dust Loading ◽  
The Absolute

Abstract. The Moderate Resolution Imaging Spectroradiometer (MODIS) onboard EOS Terra measures global aerosol optical depth and optical properties since 2000. MODIS aerosol products are freely available and are being used for numerous studies. In this paper, we present a comparison of aerosol optical depth (AOD) retrieved from MODIS with Aerosol Robotic Network (AERONET) data for the year 2004 over Kanpur, an industrial city lying in the Ganga Basin in the northern part of India. AOD retrieved from MODIS (τaMODIS) at 0.55µm wavelength has been compared with the AERONET derived AOD (τaAERONET), within an optimum space-time window. Although the correlation between τaMODIS and τaAERONET during the post-monsoon and winter seasons (R2~0.71) is almost equal to that during the pre-monsoon and monsoon seasons (R2~0.72), MODIS is found to overestimate AOD during the pre-monsoon and monsoon period (characterized by severe dust loading) and underestimate during the post-monsoon and winter seasons. The absolute difference between τaMODIS and τaAERONET is found to be low (0.12±0.11) during the non-dust loading season and much higher (0.4±0.2) during dust-loading seasons. The absolute error in τaMODIS is found to be about ~25% of the absolute values of τaMODIS. Our comparison shows the importance of modifying the existing MODIS algorithm during the dust-loading seasons, especially in the Ganga Basin in northern part of India.

scholarly journals The effect of tri hita karana culture in relationship between work stress and internal auditor performance

2019 ◽  
Vol 6 (2) ◽  
pp. 72-78 ◽  
Author(s):  
A.A. Gde Dwi Aditya ◽  
Made Gede Wira Kusuma
Keyword(s):  
Work Stress ◽  
Sampling Method ◽  
Sampling Technique ◽  
Absolute Difference ◽  
Validity And Reliability ◽  
Internal Auditor ◽  
Significance Level ◽  
Internal Auditors ◽  
The Absolute ◽  
Test Requirements

The purpose of this study was to obtain empirical evidence regarding the effect of work stress on auditor performance, and Tri Hita Karana's cultural ability to moderate the effect of work stress on auditor performance. The technique of determining the sample used is the nonprobability sampling method with a purposive sampling technique. The questionnaire is used as a method of data collection. The questionnaire is used as a method of collecting data sent to the internal auditors of Rural Banks (BPR). Of the 51 questionnaires distributed to all BPRs in Badung Regency, 43 questionnaires were feasible to analyze, with a questionnaire return rate of 94 percent and a questionnaire level that could be used at 84 percent. The hypothesis was tested at a 5 percent significance level using the Absolute Difference Value Test. The hypothesis was tested at a significance level of 5 percent using the Absolute Difference Value Test with the SPSS program. The output of the research instrument testing shows that the instrument has passed the validity and reliability test, and has fulfilled the classical assumption test requirements.

The Artful Politics of Trauma: Rancière’s Critique of Lyotard

2018 ◽  
pp. 121-141
Author(s):  
Tina Chanter
Keyword(s):  
The Other ◽  
Absolute Difference ◽  
The Sublime ◽  
The Holocaust ◽  
Singular Event ◽  
Privileged Status ◽  
Specific Meaning ◽  
Per Se ◽  
The Absolute

Just as Rancière challenges the absolute difference between politics and art, he resists the absolutization of the other that he sees as characteristic of the ethical turn in contemporary aesthetics. The tendency of Lyotard, however, remains turning alterity into the unrepresentable, the unassimilable, and the unthinkable. Its consequences are precisely what Rancière forebodes with the appropriation of the sublime: For all its talk of art witnessing that which is unrepresentable—and the holocaust as the unrepresentable per se—the ethical turn only manages to rejoin a discourse of purism. If everyone is traumatised, what specific meaning remains for trauma? This chapter explores the context of Rancière’s critique of Lyotard, particularly regarding the attenuation of any sense to trauma that accumulates a privileged status for its singular event; it subsequently interrogates the generalization of trauma to such an extent that one evacuates it of any significance.

Madhva (1238?–1317?)

2018 ◽  
Author(s):  
Valerie Stoker
Keyword(s):  
Absolute Difference ◽  
Philosophical School ◽  
The World ◽  
The Absolute ◽  
Canonical Texts

Madhva, Hindu theologian and ascetic, founded the philosophical school commonly called Dvaita Vedānta, but which Madhva and his followers termed tattvavāda, or realism. The name Dvaita refers to Madhva’s dualistic interpretation of the Hindu canonical texts known as the Upaniṣads, also known as Vedānta. In contrast to the monist and semi-monist systems of his two major Vedāntin predecessors, Śaṅkara and Rāmānuja, Madhva asserted the absolute difference between God (īśvara) and human souls (jīva), claiming that they were uncreated, eternal principles with fundamentally distinct natures. Madhva delineated the respective natures of God and souls so as to assert God’s complete transcendence of the world and to legitimate the practice of devotion as the principal means of attaining liberation from the cycle of rebirth (saṃsāra). Madhva’s realist epistemology served as the foundation for this ontological emphasis on difference (bheda).

scholarly journals Experimental research of the memory of sound impressions

2020 ◽  
Vol VI (3) ◽  
pp. 204-227
Author(s):  
N. Girshberg
Keyword(s):  
Experimental Research ◽  
Individual Characteristics ◽  
Absolute Difference ◽  
Time Intervals ◽  
The Absolute

The purpose of this work is to explore memory in relation to the pitch, depending on the different time intervals that flow between the two compared tones. Just as many other conditions affect the memory of tones, such as: duration, position and intensity of the tone, the absolute difference of the compared tones, individual characteristics and skill of the studied, then all these conditions must be made constant, the same must be changed at the same time, it must research.

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