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Resolvability in Wheel Related Graphs and Nanostructures

Thesis Info

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Author

Hafiz Muhammad Afzal Siddiqui

Program

PhD

Institute

National University of Sciences & Technology

City

Islamabad

Province

Islamabad

Country

Pakistan

Thesis Completing Year

2015

Thesis Completion Status

Completed

Subject

Natural Sciences

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/6682/1/Hafiz_Muhammad_Afzal_Siddiqui_Maths_2015_NUST_ISD.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727087916

Similar


Resolvability in graphs has appeared in numerous applications of graph theory, e.g. in pattern recognition, image processing, robot navigation in networks, computer sciences, combinatorial optimization, mastermind games, coin-weighing problems, etc. It is well known fact that computing the metric dimension for an arbitrary graph is an NP-complete problem. Therefore, a lot of research has been done in order to compute the metric dimension of several classes of graphs. Apart from calculating the metric dimension of graphs, it is natural to ask for the characterization of graph families with respect to the nature of their metric dimension. In this thesis, we study two important parameters of resolvability, namely the metric dimension and partition dimension. Partition dimension is a natural generalization of metric dimension as well as a standard graph decomposition problem where we require that distance code of each vertex in a partition set is distinct with respect to the other partition sets. The main objective of this thesis is to study the resolving properties of wheel related graphs, certain nanostructures and to characterize these classes of graphs with respect to the nature of their metric dimension. We prove that certain wheel related graphs and convex polytopes generated by wheel related graphs have unbounded metric dimension and an exact value of their metric dimension is determined in most of the cases. We also study the metric dimension and partition dimension of 2-dimensional lattices of certain nanotubes generated by the tiling of the plane and prove that these 2-dimensional lattices of nanotubes have discrepancies between their metric dimension and partition dimension. We also compute the exact value of metric dimension for an infinite class of generalized Petersen networks denoted by P(n; 3) by giving answer to an open problem raised by Imran et al. in 2014, which complete the study of metric dimension for the class of generalized Petersen networks P(n; 3).
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رسائل و جرائد

شعر و ادب کو پروان چڑھانے میں ادبی شخصیتوں کا اپنا مقام و مرتبہ ہے یہ کیسے ہو سکتا تھا کہ رسائل و جرائد اور اخبارات ان سے پیچھے رہتے خطہ سیالکوٹ کے مقامی رسائل و جرائد اور اخبارات ادب کی ترقی کے لیے ماضی سے اہم خدمات سر انجام دیتے چلے آرہے ہیں۔ان میں ’’نوائے سماج‘‘،’’ندائے سیالکوٹ‘‘،’’ہمدرد پاکستان‘‘ ،’’محنت کش‘‘ اور ’’شبنم‘‘ اہم رسائل و جرائد میں شمار ہوتے ہیں۔ان رسائل و جرائد اور اخبارات کے باقاعدہ ادبی ایڈیشن بھی شائع ہوتے رہے ہیں۔

          سیالکوٹ کے اخبارات کی موجودہ صف میں ’’صدائے شہر‘‘ ،’’نوائے شمال‘‘ اور ’’اخبار سیالکوٹ‘‘ نمایاں اخبارات ہیں۔رسائل و جرائد کی فہرست میں ’’مرے کالج میگزین ‘‘،’’مفکر‘‘،’’کاوش‘‘، ’’افق‘‘،’’محورِحیات ‘‘، ’’اقدار‘‘، ’’ادراک‘‘، ’’انتخاب‘‘، ’’کیہان‘‘، ’’یدبیضا‘‘، ’’گجر‘‘، ’’کرائیڈن‘‘، اور’’سٹی میگ‘‘آج بھی ادبی خدمات میں اہم کردار ادا کر رہے ہیں۔

          ’’گجر‘‘ ،’’انتخاب‘‘،’’ید بیضا‘‘ تاب اسلم کے شعور و فکر کا نچوڑ ہیں ان تینوں رسائل وجرائد کو تاب اسلم بڑی عرق ریزی سے ادبی دنیا کے سامنے پیش کرتے رہے ہیں۔ان ادبی رسائل نے بہت سے نئے لکھنے والوں کی راہنمائی کا فریضہ سر انجام دیا ہے۔تاب اسلم کے ان جرائد کو نہ صرف سیالکوٹ بلکہ برصغیر پاک و ہند کے نامور ادبا و شعرا ،ناقدین اور محققین کا قلمی تعاون حاصل رہا۔سیالکوٹ کے اہم ادبی رسائل و جرائد کے تعارف کے لیے تفصیل پیش کی جاتی ہے۔

۱۔       مر ے کالج میگزین :

          مرے کالج میگزین کا پہلا شمار ہ نومبر...

برصغیر میں عربی ادب کا تحقیقی جائزہ اور اس کے اثرات

At the time of arrival of Muslim community in Sub-Continent Region and due to their settlement in the region Arabic Language has been prevailed and such as the system of its publication and learning has been commenced. Because the directives of Islam and laws are in the Arabic Language as per Quran & Sunna so that it is necessary to learn the Arabic language for the awareness of Islamic directions. So that to achieve the knowledge of Sharia inclu-ding the expertise the peoples of Sub-continent has been achieved the expertise of Arabic language, literature, knowl-edge Ilmul Saraf al-khawa, knowledge of al-ishtiaq & Ilmul Balaghta etc. Moreover it is clarify that Scholar of religious have shown their expertise so that the scholar of Arab have been convinced their expertise. The basic point of service in Arabic Language of Scholars of Sub-Continent that they do not served only to enhance the language but the cause of service was to serve themselves on religious matters and represents themselves on work hard and tried themselves to achieve the better performance of identification of Islam.  A positive result and effects have been achieved as a sun shining of Islam is remaining and its waves are enhancing all around the world such as the sun shining of Islam is remained in Arab world such as the publication of literature is also remaining in the Sub-Continent region in the actual shape and saved. Because the Islam will remain till the day of judg-ment and its representatives/workers will born till the date such as the scholars of literatures will also born and they will save the knowledge of Arabic.  They will alive till the Day of Judgment.

Identification of Susceptibility Genes Involved in Rheumatoid Arthritis and Systemic Lupus Erythematosus

Rheumatoid arthritis (RA) is a common multifactorial and systemic autoimmune disease characterized by inflammation of synovial fluid which leads to sever pain and progressive joints and bones destruction and even disability if left untreated. The etiology of RA is very complex and is suggested to be the outcome of various environmental, genetics and hormonal factors. Several genes have been identified in which the underlining mutation and polymorphisms result in this complex trait. The incidence and prevalence of RA is increasing worldwide including Pakistan, therefore, the objective of the present work was to examine Pakistani population for identification of susceptible genes and variants which are involved in onset of RA. The progression pattern of RA may exhibit ethnic variations due to differences in environmental factors and genetic pre-disposition of the individuals. Therefore, a cross sectional study was conducted on 500 RA patients (mean age at onset of disease, 39.1±13.0 years) which was aimed to estimate the progression pattern with keeping in mind the severity of disease in the Pakistani patients. It was found that, in general, RA preferentially affects women with female to male ratio of about 3:1; however, patients with above 60 years of age have equal female to male ratio. The disease severity increases with increase in the age and reaches to its peak in patients above 60 years of age (p=0.001). Rheumatoid arthritis susceptibility loci/gene were genotyped in a sample of 366 Pakistanis that comprised related and unrelated cases and controls. Findings from this part were compared with other studies to determine whether the same biological pathways are involved in determining the RA risk in different population groups. The genotyping was performed using the TaqMan assays and the results were analyzed with family case-control (FamCC) software. Twelve of the 33 SNPs/31 loci were associated in this sample with significant p- values ranging from 7.05E-06 to 3.72E-02, the most significant being the KIF5A- PIP4K2C/rs1678542 SNP. Some loci with possible and suggestive association signals were also identified. Since, CTLA4 is one the important genes implicated in many autoimmune diseases including RA and SLE, therefore, entire CTLA4 gene including 1000bp flanking region both from 5'' and 3'' ends was sequenced in 95 RA and 95 SLE patients to identify functional rare variants (MAF<0.05) and common variants (MAF≥0.05). A total of 38 variants were identified in both RA and SLE patients; in which 21 were already reported in publically available databases (CHIP Bioinformatics, dbSNP) and remaining 17 were novel variants. Association of PPARG gene was tested with RA in Pakistani individuals. PPARG-Pro12Ala polymorphism was genotyped in 300 Pakistani case-control sample using ARMS-PCR method and data was analyzed through Graphpad Prism 5V software. Significantly higher frequency of homozygous genotype (GG; AlaAla) was observed in cases as compare to controls [27 (18.0%) vs 5 (3.3%); χ2 18.54; p < 0.0001] which suggests that GG genotype might contribute to RA in the Pakistanis. Furthermore, significantly higher allele frequency was observed for G allele (Ala) (a minor allele) in cases having same trend and direction of association [p < 0.0001, OR 1.991(1.412-2.808), Z-test value 4.008] . Individuals from 12 large RA families were selected for linkage analysis and were screened through commercially available automated linkage panel. HumanLinkage V Panel Set GoldenGate Assay from Illumina having 6,056 SNP markers with 0.62cM average distance between the SNPs was used. Data was checked for quality controls and is being analyzed for LOD score calculation.