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On Irregular Total and Graceful Labelings

Thesis Info

Access Option

External Link

Author

Siddiqui, Muhammad Kamran

Program

PhD

Institute

Government College University

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2012

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/2438/1/2551S.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726797438

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A graph labeling is an assignment of integer label to the elements of graph in such a way that some certain conditions are satisfied. If the domain set consists only vertices (or edges) then it is called vertex (or edge) labeling respectively. If the domain set consists vertices and edges then it is called total labeling. A graceful labeling of a (p, q)-graph is an injection f from the set of vertices to the set {1, 2, . . . , q + 1} such that each edge uv is assigned the label |f (u) − f (v)|, the resulting edge labels are distinct. Moreover if f has the property that there exists an integer λ such that for each edge uv either f (u) ≤ λ < f (v) or f (v) ≤ λ < f (u) then f is called an α-labeling. A one-to-one map taking the vertices on the integers 1, 2, 3, . . . , p with the property that the edge weight (sum of end points labels ) form an arithmetic progression starting from a and having common difference d, is called (a, d)-edge antimagic vertex labeling. A total k-labeling of a graph G is a labeling from the set of vertices and edges to the set {1, 2, . . . , k}. A total k-labeling is defined to be an edge irregular total k-labeling of the graph G if edge weights are different for all pairs of distinct edges. The minimum value of k for which the graph G has an edge irregular total k- labeling is called the total edge irregularity strength of the graph G, denoted by tes(G). In this thesis, we construct an α-labeling of trees from graceful labeling of smaller trees and using a connection between α-labeling and edge antimagic vertex labeling we obtain a super (a, d)-edge antimagic total labeling of trees. Moreover we present new results on the total edge irregularity strength.
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مولانا عثمان احمد قاسمی

آہ ! مولانا عثمان احمد قاسمی چل بسے
۴؍ رمضان المبارک ۱۴۱۸؁ھ کو راقم الحروف کے ایک کرم فرما اور دارالمصنفین کے ہمدرد مولانا عثمان احمد قاسمی اﷲ کو پیارے ہوگئے، اس کی اطلاع موصوف کے حقیقی بھانجے ڈاکٹر محمد اسامہ کے ایک خط سے ہوئی جو انتقال کے دو ہفتے بعد ملا، یہ خبر سخت تکلیف دہ تھی اور جنازہ کی شرکت سے محرومی کا تو ہمیشہ ملال رہے گا۔
شاہ گنج اور جونپور کے وسط میں پختہ سڑک کے قریب ہی غوری النسل لوگوں کی مشہور بستی پسری ان کا آبائی وطن تھا۔ ان کے جدامجد حضرت سلطان شاہ، ٹانڈہ کے مشہور صاحبِ دل بزرگ حضرت چاند شاہ کے اجل خلفاء میں تھے جو نقشبندی سلسلے سے منسلک تھے اور فیض آباد ہی نہیں اعظم گڑھ، جونپور اور سلطانپور وغیرہ کے لوگوں کو بھی ان سے بڑا فیض پہنچا۔
پسری کا یہ خاندان علمی، دینی اور دنیاوی لحاظ سے فائق تھا۔ مولانا عثمان احمد قاسمی کے جدبزرگوار کے حسبِ ذیل تین صاحبزادے تھے، مولانا عبدلغفور صاحب، مولانا دین محمد صاحب، مولانا شاہ سعید احمد صاحب، موخرالذکر کے پانچوں بیٹے دینی تعلیم سے بہرہ ور ہوئے، ان میں بڑے مولانا جمیل احمد فخرِ خاندان تھے اور سب سے چھوٹے یہی مولانا عثمان احمد تھے، مولانا دین محمد صاحب بھی عالم، اچھے استاد اور نہایت باغ و بہار شخص تھے، یہ مولانا ابوالعرفان ندوی سابق مہتمم دارالعلوم ندوۃالعلماء کے پدر بزرگوار تھے، علم و دین کی اشاعت ان کی زندگی کا خاص مشغلہ تھا، جونپور کی اٹالہ مسجد کا مدرسہ ان کے اہتمام کے زمانے میں بڑی رونق پر تھا۔
مولانا دین محمد صاحب کی جدوجہد سے شاہ گنج کی جامع مسجد میں بھی ایک دینی مدرسہ بدرالاسلام کے نام سے قائم ہوا، جس کے وہی سارے انتظامات اور تعلیمی خدمات انجام دیتے رہے مگر جب...

حرية الفكر والتعبير عند الإمام بديع الزمان سعيد النورسي رحمه الله

The freedom of thought and expression has acquired a diversity of meanings and limitations determined by the evolving socio-historical contexts of various civilizations through the history. This piece of research briefly investigates the history of evolution of this concept in Islamic and Western intellectual circles and then intends to focus upon the elaboration of this idea by Imam Badi-uz-Zaman An-Naurasi. Iman Naurasi supports the human right of thinking and expressing ideas freely but at the same time recognizes the need of divine intervention in delimiting its boundaries. Humans, if left entirely unrestricted to make their choices in life, would only bring about disastrous results and thus lead to cessation of a collaborative social life. Therefore, Imam proposes that humanity should abide by some universal principles and high moral values inspired by the divine revelation so that the society could collectively ensure the pursuit of human progress and well-being. Imam proves his point through the instances from the Islamic history that divinely guided freedom of thought and expression provided the world with a vivid model of life which provided people the rights of choosing everything in their life ranging from faith to marital and economic decisions.

Relationship Between Understanding and Practices About Assessment Among Elementary School Mathematics Teachers in Karachi

Assessment enables teachers to assess students' learning and utilizes the information to improve students' learning and teachers' teaching practices (Harris, Irving, & Peterson, 2008). Therefore, teachers' conceptions of assessment have become critical aspects in any educational system because evidence exists that teachers' conceptions influence how they teach and what students learn. The study investigated the relationship between mathematics teachers' conceptions regarding assessment and their assessment practices in private schools of Karachi, Pakistan. Furthermore, this study explored the differences between primary and middle school mathematics teachers' conceptions about assessment and how such teachers' conceptions regarding assessment translated into their practice. A cross-sectional survey using the 'Teachers' Conceptions of Assessment' (TCoA) questionnaire was conducted on primary and middle level mathematics teachers (n=155) of schools which had an ongoing link with AKU-IED in sending their teachers for professional development courses. Data were analyzed using correlations and the non-parametric version of the independent t-test (i.e., Mann-Whitney). Results indicate that teachers' conceptions about assessment were positively correlated (r=.780) with their assessment practices which is statistically significant (p<.001). A further dimension to this study that evolved was its qualitative component which explored the contrasting conceptions of a group of participants regarding their assessment practices. Qualitative data were collected through unstructured observations and discussions with participant teachers. Participants with progressive views about assessment focused more towards improving teaching and learning. However, teachers who had limited conceptions towards assessment focused more on judging rather than improving students' learning. Overall results indicate that participant teachers agreed most with the improvement conception and accountability conception and disagreed with the irrelevance conception. Improvement, school, and student accountability conceptions were positively correlated. The irrelevance conception was inversely related to the improvement conception. Moreover, it was found that both primary and middle level mathematics teachers had positive conceptions towards assessment but no statistically significant differences were found between their conceptions of assessment. Thus, the study suggests that teachers with limited conceptions of assessment can be helped through professional development sessions and short educational measurement courses. The study provides opportunities for future researchers to conduct studies with larger, more representative samples for generalizability.