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Topological Invariants of Graphs

Thesis Info

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Author

Nadeem, Imran

Program

PhD

Institute

COMSATS University Islamabad

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2019

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/12761/1/1.%20Final%20Thesis_Signed_Topological%20Invariants%20of%20Graphs%2c%20Imran%20Nadeem%2c%20CIIT%20FA13-PMATH-003%20LHR.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727618532

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Chemical graph theory provides useful tools such as molecular descriptors to develop strong intrinsic relationship between the physicochemical features of chemical compounds and their molecular graphs. The study of molecular descriptors provides a theoretical basis for the fabrication of chemical materials and is helpful in making up for the lack of chemical experiments. There are two prominent types of molecular descriptors; the topological indices and counting polynomials. Further, topological indices can be categorized in two major classes: one class is based on degree and the other class is based on distance. In this thesis, we present the study of certain topological indices belonging to degree- and distance-based classes and counting polynomials for some well-known nanostructures. We also present a comparative study between different topological indices belonging to degree- and distance-based classes for general graphs. In addition, we study the para-line transformation of graphs and obtain the general expressions of certain topological indices for this transformation. We achieve the lower and upper bounds of certain distance-based topological indices for the para-line transformation of graphs.
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پروفیسر محمد رضوان علوی

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لکھنو کی علمی، تعلیمی اور ادبی سرگرمیوں سے بھی سروکار رکھتے تھے۔ ان میں علمی و انتظامی دونوں طرح...

امنا عائشة ملكة العفاف رضي االله عنها

This research aims to explore various features of Syyidah some highlights paper This. Personage noble s'(ر الله عا) ishah‘A’ distinguished aspects of her biographical account, her extraordinary intelligence, eminent rank amongst other wives of the Prophet Muḥammad (r), excellence over women of the world and being mentioned in the Qur’ān for her praiseworthy character. The scholarly areas, in which, she outshone others in Islamic intellectual heritage, include the Quranic exegesis, Ḥadīth narratives, jurisprudence, scholastic reasoning: analysis of jurisprudential methodology and principles of deduction of rulings and opinions. She adopted multifarious modes in this regards including explicit, direct, generalized, inductive and analogous approaches in the Islamic intellectual scholarship. By acknowledged was (ر الله عا) ishah‘A of grandeur The the companions of the Prophet, her scholarly point of view in conciliation of the problems of the Qur'ān and Ḥadīth made her stand out amongst all. She was a keen researcher, peaceful preacher and the greatest scholar of Islām of all times. Her knowledge and command over religious and social matters made her one of the most reliable experts of the Qur'ān, Ḥadīth and Fiqh. Such was her stature as the archangel Jibrā’īl presented his salutation to her.

Design Features of Monolingual Urdu Pedagogical Dictionary for Advanced Learners of Urdu Language

Design Features of Monolingual Urdu Pedagogical Dictionary For Advanced Learners of Urdu Language The lexicographic tradition in Monolingual Urdu Dictionaries is very old but the implications of modern postulates of lexicography are not evident in compiling Urdu monolingual dictionaries. The present study deals with a description of design features of a pedagogical monolingual Urdu learners’ dictionary for the advanced learners of Urdu on the tradition set by the COBUILD dictionary. Basically the study looks at three perspectives: the opinions of the user (learners and teachers of Urdu) of monolingual Urdu dictionaries, assessing the possibilities of collecting a database or corpus of Urdu as a basis of a monolingual advanced learners’ dictionary of Urdu and design features of a pedagogical Urdu monolingual advanced learners’ dictionary. The study is descriptive. The data regarding the opinions of the learners and teachers of Urdu was collected through a questionnaire. The theoretical framework was based on the questionnaire based studies conducted by Diab (1998) and Iqbal (1987). The responses collected from the teachers and learners of Urdu were statistically analyzed by securing the mean score against each statement. The second perspective of the study was to see how far it is possible to collect a corpus of Urdu as a basis of a monolingual learners’ dictionary of Urdu. A number of studies (The EMILLE Project 2004, Becker & Riaz 2002, Anwer, Wang & Wang 2006, Hussain & Ijaz 2008, Hussain 2008, Chohan & Bukhari 2009) have been reported in the area of Urdu corpus. CRULP (Center of Research in Urdu Language Processing) collected a corpus of 19 million words which is used to design an Urdu-English dictionary. These studies maintain that there is a great potential as far as the collection of a corpus is concerned. The third and the central concern of the study is to design the features of a pedagogical monolingual learners’ dictionary for advanced learners of Urdu language and for this purpose the design features of the COBUILD dictionary were taken as model. This choice is made on the grounds that this dictionary is meant both for teachers and students; it bears some unique features in its design and has got the appraisal of many critics (see Boguraev 1990, Aarts & Meijs 1990, Krishnamurthy 2002, 2001). Moreover the results drawn from the above mentioned surveys of both the learners and teachers of Urdu also provided insights to determine the essential features of a pedagogical monolingual learners’ dictionary for the advanced learners of Urdu. The results concluded that there is a great need to design a monolingual learners’ dictionary for advanced learners of Urdu and the compiling a corpus based monolingual Urdu learners’ dictionary for advanced learners will bring innovative changes in learning and teaching of Urdu and lexicographic tradition of Urdu. Finally, the design features of a pedagogical monolingual Urdu dictionary for the advanced learners of Urdu were established. These features were based on these aspects: the possibility of the application of the method adopted in the COBUILD and the possibility of collection the corpus of Urdu and the availability of the technical and technological needs while collecting the corpus of Urdu. The study concluded that greater possibilities are there to collect a corpus of Urdu and the selected model of COBUILD dictionary can also b applied on a corpus based monolingual Urdu dictionary for advanced learners of Urdu.