THE HARMONIOUS, ODD HARMONIOUS, AND EVEN HARMONIOUS LABELING

Suppose  is a simple and connected graph with  edges. A harmonious labeling on a graph  is  an injective function  so that there exists a bijective function  where  for each  An odd harmonious labeling on a graph  is an injective function  from  to non-negative integer set less than  so that there is a function  where  for every  An even harmonious labeling on a graph  is an injective function  so that there is a bijective function   where  for each . In this paper, we discuss how to build new labeling (harmonious, odd harmonious, even harmonious) based on the existing labeling (harmonious, odd harmonious, even harmonious

Harmonious Coloring of Trees with Large Maximum Degree

A harmonious coloring of $G$ is a proper vertex coloring of $G$ such that every pair of colors appears on at most one pair of adjacent vertices. The harmonious chromatic number of $G$, $h(G)$, is the minimum number of colors needed for a harmonious coloring of $G$. We show that if $T$ is a forest of order $n$ with maximum degree $\Delta(T)\geq \frac{n+2}{3}$, then h(T)= \Delta(T)+2, & if $T$ has non-adjacent vertices of degree $\Delta(T)$; \Delta(T)+1, & otherwise. Moreover, the proof yields a polynomial-time algorithm for an optimal harmonious coloring of such a forest.Comment: 8 pages, 1 figur

Harmonious architecture and kinetic linear energy

This is a chapter in a book based upon the work from an Erasmus International Project which took place in Athens in July 2012

Odd Harmonious Labeling of Some Graphs

The labeling of discrete structures is a potential area of research due to its wide range of applications. The present work is focused on one such labeling called odd harmonious labeling

Passion and exercise addiction: Healthier profiles in team than in individual sports

New evidence suggests that passion is linked to exercise addiction. The objective of this work was to determine the strength of the relationship between exercise addiction, obsessive passion, and harmonious passion in team versus individual sports. Athletes (n = 190) from three team and three individual sports were examined. Results of hierarchical multiple regressions revealed that obsessive passion and harmonious passion were significant (p < .001) predictors (R2 = .39) of exercise addiction. Obsessive passion accounted for 25% and 50% of the variance in team and individual sports, respectively. Harmonious passion added little to the shared variance (3–4%). The levels of risk for exercise addiction were identical (15%) in the two groups. In team sports, harmonious passion was higher than in individual sports (p < .001). The current results suggest that profiles of passion in team sports are superior to those in individual sports, while the risk for exercise addiction is similar

How dental students’ course experiences and satisfaction of their basic psychological needs influence passion for studying in Chile

Purpose: This study aimed to determine how the general course experiences of dental students in Chile and the satisfaction or frustration of their basic psychological needs influenced their passion for studying, and how passion influenced students’ study strategies. Methods: A correlational cross-sectional study was conducted at 3 Chilean dental schools between April and June 2018, in which 935 undergraduate students participated. Students responded to Spanish-language versions of 4 psychological scale tools: the Course Experience Questionnaire, the Basic Psychological Needs Satisfac¬tion and Frustration Scale, the Passion Scale, and the Revised Study Process Questionnaire. Data were analysed with bivariate correlations and structural equation modelling, controlling for age, gender, year of study, and type of university. Results: Students’ general course experiences (i.e., good teaching, clear goals and standards, appropriate assessment, and appropriate workload) positively predicted basic need satisfaction and negatively predicted need frustration. Need satisfaction positively predicted passion in students, with stronger scores for harmonious passion. Basic need frustration positively predicted obsessive passion and negatively predicted harmonious passion. Harmonious passion positively predicted deep study strategies and negatively predicted surface study strategies, while obsessive passion positively predicted both deep and surface study strategies. Conclusion: Dental students’ optimal course experiences positively influenced the satisfaction of their basic psychological needs, which favoured harmonious over obsessive passion. In turn, harmonious over obsessive passion positively influenced deep study strategies. Therefore, efforts should be made to provide course experiences that support students’ basic needs and harmonious passion for studying, both in classroom and chair-side teaching