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On Irregular Total Labelings

Thesis Info

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Author

Ali Ahmad

Supervisor

Martin Baca

Program

PhD

Country

Pakistan

Thesis Completing Year

2005

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/614

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726797865

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A labeling of a graph is a map that carries graph elements to the numbers (usually positive or non-negative integers). The most common choices of domain are the set of all vertices (vertex labelings), the edge set alone (edge labelings), or the set of all vertices and edges (total labelings). In many cases, it is interesting to consider the sum of all labels associated with a graph element. It is called the weight of the element: the weight of a vertex or the weight of an edge. In this thesis, we consider a total k-labeling as a labeling of the vertices and edges of graph G with labels from 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 and to be a vertex irregular total k-labeling of G if vertex-weights are different for all pairs of distinct vertices. 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, tes(G). Analo- gously, the total vertex irregularity strength of G, tvs(G), is defined as the minimum k for which there exists a vertex irregular total k-labeling of G. In this thesis, we present new results on the total edge irregularity strength and the total vertex irregularity strength.
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یکم مئی: یومِ مزدوراں

یکم مئی : یومِ مزدوراں
نحمدہ ونصلی علی رسولہ الکریم امّا بعد فاعوذ بااللہ من الشیطن الرجیم
بسم اللہ الرحمن الرحیم
معزز اساتذہ کرام اور میرے ہم مکتب شاہینو!
آج مجھے جس موضوع پر اظہار خیال کرنا ہے وہ ہے:’’یکم مئی: یومِ مزدوراں‘‘
جناب صدر!
یوم مئی ایک ایسے دن کی یاد دلاتا ہے جس دن انسانیت کے ساتھ ظلم روا رکھا گیا ، جس دن انسانیت کی تذلیل کی گئی، جس دن انسانیت کے ساتھ خون کی ہولی کھیلی گئی ، جس دن مفلوک الحال طبقہ کو گولی کا نشانہ بنایا گیا۔
تو قادر و عادل ہے مگر تیرے جہاں میں
ہیں تلخ بہت بندۂ مزدور کے اوقات
صد رِمحترم!
مزدور کی ایک شان ہے، مزدور کی ایک آن ہے، مزدور کو اللہ کا قرآن اور حضورؐ کی حدیث عزت دے رہی ہے، مزدور الکاسب حبیب اللہ کے تحت اللہ کا دوست ہوتا ہے۔ مزدور کیمحنت ہی سے بزم کائنات کاحسن نکھرتا ہے۔
؎ ان کے دم سے شیش محلوں میں ہے قائم روشنی
جنابِ صدر!
مزدور کے ہاتھوں سے شجر ہستی میں تازگی آتی ہے، مزدور کے ہنر سے چمنِ حیات میں پھول کھلتے ہیں، مزدور کی طاقت سے ہی کو ہساروں میں آبشار یں پیدا ہوتی ہیں، مزدور کی محنت سے ہی فصلیں کشت ِزعفران بنتی ہیں، مزدور کے ہاتھوں سے ہی دریاؤں میں روانی آتی ہے۔
صدرِذی وقار!
امریکہ کے شہر شکاگو میں مزدوروں نے جان کا نذرانہ پیش کر کے رہتی دنیا تک اپنا نام زندہ کیا، بقائے دوام حاصل کر لیا، ظلم و استبداد کی چکی میں پسے ہوئے مزدور انسانیت کے لیے خوشی کی نوید جاں فزا ثابت ہوئے ، شب وروز افسردہ ذہنوں میں تروتازگی کے تصورات پیدا کیے۔
جنابِ صدر!
انسان کو آرام کی بھی ضرورت ہوتی ہے۔ مسلسل کام ، کام...

خون حرا م ہے: حلال انڈسٹری کے بنیادی قرآنی معیار کا تحقیقی جائزہ

Healthy nourishment depends on healthy food. General consideration of people is of being the food safe and edible for human consumption not its effect on their spiritual selves but the Islamic terms Ḥalāl and Ḥarām emphasis on both physical and internal safety. Islam commands to avoid doubtful and dubious things rather than to use Ḥarām. The unprecedented evolution and advancement of science and technology caused a revolution in the food-science and technology as well. Many new and innovative flavors etc. Took place of organic and natural consumables. Accordingly, the Muslims were in dire need of a robust system which would be able to convince them of the Ḥalāl status of the daily consumables. The article investigates the Sharī’ah stand on the issue of blood in the light of Qur’ān, Sunnah and comparative jurisprudence study, and modern sciences related to blood. Keeping in mind the Globalized Halal Industry all the researched is coupled with combined comparative study of all Schools of Islamic Fiqh, to make easy the way of Unified Halaal Standard regarding the blood. Under the main title The paper comprises subtopics of an introduction and few chapters, which deal with definition and functions of blood, types of blood, difference between blood of aquatic and land animals, comparative study of modern sciences related to blood and Shariah status of use of the blood in various industries in term of Halal and Haram.

Pre- Clinical and Clinical Evaluation of Folk Medicinal Plants of Cholistan Desert for Antidiabetic Activity

Diabetes mellitus (DM) is a chronic disease and one of the most important public health challenges facing mankind. The use of the folkloric remedies for the wellbeing of the mankind has been in practice since ancient times. Citrullus colocynthis (Cucurbitaceae), Capparis decidua (Capparaceae) and Fagonia cretica L. (Zygophyllaceae) are the medicinal plants used widely in Punjab, Pakistan. A recent survey has demonstrated that traditional healers and herbalists frequently use these plants to treat diabetes. Initially all the three plants were characterized in vitro and in vivo animal studies to identify the most potent plant amongst these. In the current study, the traditional medicine (TM) of the most effective plant (Fagonia cretica L.) was prepared as a tea and the profile of the main metabolites present in TM, was analyzed via LC/MS/MS. The TM inhibits α-glucosidase in vitro with an IC50 of 4.62±0.27 μg/ml. The hypoglycemic effect of the TM was evaluated in normoglycemic and Streptozotocin-Nicotinamide treated diabetic rats, using glibenclamide as internal control. The hypoglycemic effects were observed upto 3 hrs. The preparation (250 or 500mg/kg body weight) was administered one a day for 21 consecutive days. The dose of 500mg/kg was effective in the management of the disease causing a 45% decrease in plasma glucose level at the end of experimental period on Day 21. Histological analysis of pancreatic sections confirmed that STZ/NIC treatment caused destruction of pancreatic islet cells while pancreatic sections from treatment groups showed that both the extract and Glibenclamide partially prevented this deterioration. The mechanism of this protective effect is unclear. The radical scavenging potential of the ethyl acetate fraction (93%) and the cytotoxic efficiency (4.7±0.21) of the dichloromethane fraction is an edge of Fagonia cretica L. over the other plants under investigation. However, such a finding coupled with the safety profile observed by the biochemical parameters as marker of toxicity, suggests that ingestion of the tea could confer addition benefits and should be investigated further. The formulated tablets of Fagonia cretica L. lyophilized powder showed the physical variables of the formulation (Weight variation, Hardness, Friability and Disintegration) within the pharmacopoeial (BP) limits. The clinical trials of the formulation conducted at Bahawal Victoria Hospital, Bahawalpur have further proven the efficacy of this folkloric medicinal plant in the management of the disease. Fasting and postprandial blood glucose levels coupled with glycosylated haemoglobin levels (HbA1c -an excellent tool to assess the glycemic control over the entire period of time) confirms the claims made by the local healers of the area. Glycaemic control and the safety profile at preliminary levels suggest the incorporation of this folkloric remedy of the area into the treatment options for the management of the disease. However long term clinical trials on lager number of subjects and safety profile for a longer period of time are necessary elements for the integration of this important plant into the main stream treatment options. We have the faith on the basis of the undertaken studies that use of the remedy made from lyophilized powder of the plant extract could be a supportive tool for the claim made by the local healers for the management of disease in Pakistan.