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H- Magic Behaviors of Some Graphs

Thesis Info

Access Option

External Link

Author

Cheema, Imran Zulfiqar

Program

PhD

Institute

COMSATS University Islamabad

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2018

Thesis Completion Status

Completed

Subject

Statistics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/11281/1/Imran_Zulfiqar_Cheema_soft_copy_for_upload.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726353115

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A graph ( , ) G V E has an H -covering if every edge in Ebelongs to a subgraph of G isomorphic to H . SupposeG admits an H -covering. AnH -magic labeling is a mapping l from ( ) ( ) E G V G È onto the integers {1,2,...,| ( ) ( )|} E G V G È with the property that, for every subgraph Aof G isomorphic toH , there is a positive integer csuch that ( ) ( ) ( ) ( ) . v V A e E A A v e c ll ÎÎ = å + å =å A graph which possess such type of labeling is known as H -magic graph. Further if in a graph vertices are labeled first with smallest positive numbers, then the graph is called H -supermagic. Moreover a graph is said to be H -( , ) ad-anti magic if the magic constant for an arithmetic progression with initial value aand a common difference . d Numerous results on labeling of many families of graphs have been published. In this thesis, research work focuses on to formulate cycle 3 C -( , ) ad anti-supermagic labeling for the MultiWheels graph, supermagic labeling for isomorphic copies with its disjoint union of Multi-Wheels graph and cycle ( , ) ad-anti-supermagic labeling for Web graph. Also cycle anti-supermagic labeling for isomorphic copies with its disjoint union of ladder and triangular ladder graphs have been formulated. In addition, investigation of fan, friendship, ladder and wheel line graphs and study of the supermagic and anti-supermagic vertex-edge-face labeling of such graphs and their isomorphic copies have been carried in this thesis. An anti-supermagic labeling of the extension of cycle graphs is also formulated.Lastly the face supermagic labeling of (1,1,1) type of subdivided triangular ladder graph, subdivided 4 mC -snake graph and subdivided 4 kmC -triangular snake graph with its (1,1,...,1) and (2,2,...,2) string are also the part of this thesis.
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نواب حاجی محمد اسحا ق خان بہادر

نواب حاجی محمد اسحاق خان بہادر

(مولانا عبدالسلام ندوی)

            نہایت افسوس ہے کہ علی گڑھ کالج کے آنریری سیکریٹری نواب حاجی محمد اسحاق خان بہادر نے پچھلے مہینے دل کی حرکت بند ہوجانے سے دفعتہ انتقال کیا، مرحوم مختلف خوبیوں کے بزرگ تھے اس لئے قوم میں مختلف حیثیتوں سے ان کا ماتم کیا جارہا ہے، ہم بحیثیت ایک علم دوست بزرگ کے ان کی موت پر آنسو بہاتے ہیں۔ (نومبر ۱۹۱۸ء)

 

SCHOOL BUSINESS MANAGEMENT COMPETENCIES FOR IMPROVED ADMINISTRATIVE EFFECTIVENESS IN PUBLIC SECONDARY SCHOOLS IN RIVERS STATE NIGERIA

The study investigated school business competencies for improved administrative effectiveness in Public Secondary School in Rivers State. Three research questions and two null hypotheses were formulated to guide the study. The population of the study was 286 principals in all the public secondary schools in Rivers State. A sample of 166 through a stratified random technique was determined using the Taro Yamane formula. The instrument of the study was a self design instrument captioned “School Business Management Competencies Questionnaire (SBMCQ) and Principal Administrative Effectiveness (PAE) with the reliability coefficients of 0.77 and 0.84 respectively which was determined through the Cronbach alpha statistics. Mean scores and standard deviation was used to answer the research questions while Pearson Product Moment Correlation Coefficient was sued to test the hypothesis. It was discovered that the highest kind of business available in the public school is related to cafeteria / canteen services and that also to a high extent, resourcefulness as a business management competency improves administrative effectiveness in public secondary schools in Rivers State. It concluded that for the school administrators to manage the school business effective (administrative effectiveness), they must possess the core competence of resourcefulness, conceptual thinking and administrative organisation. It was recommended among others that the principal should have a comprehensive understanding of the school complex nature and also think critically at both abstract and concrete level to harmonize a rather multifaceted business challenges in the school and proffer realistic solutions.

Ascertainment of Governance Dynamics and Financial Liberalization on Financial Intermediation and Economic Growth: Empirical Evidence from Selected South Asian Countries

A better functioning financial sector matters directly for growth and contributes indirectly for poverty alleviation and welfare in Least Developed Countries (LDCs), through managing liquidity risk, acquisition of information, resource allocation, monitoring investment projects, saving mobilization, and facilitating exchange of goods and services. A vast variety of literature deals with the analysis of performance of financial institutions and their outcome for developing countries, especially in the context of South Asian and African region. However after the global financial crisis there emerged a need to re-examine the issues and outcomes resulting after financial liberalization process pursued by these economies. Studies conducted in this context suggested that there is a need to build a sound institutional framework which could prove to be productive for growth and welfare performance of LDCs. With this background, present analysis is a re-examination of relationship between financial liberalization (FL), financial intermediation (FD), and economic growth indicators, while taking the interference of governance (GOV) indicators into the analysis. This dissertation aims to ascertain whether financial liberalization has had any impact on financial deepening and economic growth. To carry out this empirical analysis, study utilized time series data set over the period 1995 to 2012 (based on the availability of data for specific countries), a sample of seven South Asian countries and applied Generalized Method of Moment (GMM) system analysis for estimation. To measure the financial liberalization, financial intermediation and governance, Chinn-Ito index, domestic credit to private sector and world governance indicators (WGI) are used respectively. The analysis found a positive and insignificant relation between financial deepening and financial liberalization, however, the impact of governance indicator on financial deepening has been found to be negative and robust. Moreover, as per the individual dimensions of governance are concerned, political stability and government effectiveness are important in determining the financial development among other dimensions The interaction of governance indicator and financial liberalization term yielded significant and negative impact. In the context of legal origin, findings supported that countries with mixed legal system are more financially developed and the interaction of legal origin and FL has found to be positive showing that FL castes positive impact on FD in the countries with mixed legal system. In addition, as per the results of control variables, openness of trade has positive and significant impact on financial development and it has been verified that simultaneous opening of trade and financial sector also have positive and significant impact. Inflation and government spending have expected negative and positive link respectively, and their signs are supported theoretically. Finally, in growth equation, it has been found that economic growth is important for determining the financial development.