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Construction Methods for Edge-Antimagic Labelings of Graphs

Thesis Info

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Author

Shafiq, Muhammad Kashif

Program

PhD

Institute

Government College University

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2005

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/296

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676725785151

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A labeling of a graph is a mapping that carries some set of graph elements into numbers (usually positive integers). An (a, d)-edge-antimagic total labeling of a graph, with p vertices and q edges, is a one-to-one mapping that takes the vertices and edges into the integers 1, 2, . . . , p + q, so that the sums of the label on the edges and the labels of their end vertices form an arithmetic progression starting at a and having difference d. Such a labeling is called super if the p smallest possible labels appear at the vertices. This thesis deals with the existence of super (a, d)-edge-antimagic total labelings of regular graphs and disconnected graphs. We prove that every even regular graph and every odd regular graph, with a 1- factor, admits a super (a, 1)-edge-antimagic total labeling. We study the super (a, 2)- edge-antimagic total labelings of disconnected graphs and present some necessary conditions for the existence of (a, d)-edge-antimagic total labelings for d even. The thesis is also devoted to the study of edge-antimagicness of trees. We use the connection between graceful labelings and edge-antimagic labelings for generating large classes of edge-antimagic total trees from smaller graceful trees.
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مجاہدِ ملت مولانا حفظ الرحمن

مجاہد ملّت مولانا حفظ الرحمن
(جمعیۃ علمائے ہند کی آخری شمع بجھ گئی)
جس حادثہ کا دھڑکا عرصہ سے لگا ہوا تھا، بالآخر وہ پیش آہی گیا، اور مجا ہد ملت مولانا حفظ الرحمن صاحب ۲؍ اگست ۱۹۶۲؁ء کو صبح صا دق کے وقت اپنے رب کے حضور میں حاضر ہو گئے، موت کوئی غیر معمولی واقعہ نہیں، ہر وقت اس کا بازار گرم ہے، روزانہ ہزاروں لاکھوں انسان مرتے رہتے ہیں، مگر کسی کو اس کا احساس بھی نہیں ہوتا، لیکن بعض موتیں وہ ہو تی ہیں جن سے ایک قوم اور ایک ملت کی پوری عمارت متزلزل ہوجا تی ہے، مولانا حفظ الرحمن صاحب کی وفا ت بھی انہی میں سے ہے:
فما کان قیس ھلکہ ھلک واحد ولکنہ بنیان قوم تھدما
ان کی موت سے ہماری قو می و ملی عما رت کا بہت بڑا ستون گرگیا، مولانا کی پوری زندگی اور زندگی کا ہر لمحہ ملک وملت کی خدمت میں گذرا حتیٰ کہ مرضِ الموت میں بھی اس سے غافل نہ رہے اور اپنی ان تھک محنت سے اس راہ میں جان تک دیدی، اس لیے اگر زندگی میں وہ مجاہد ملت تھے تو موت کے بعد شہید ملت ہیں۔
ان کی پوری زندگی ایک سعی پیہم اور جہد مسلسل تھی، جس سے ان کو ہندوستان کی آزادی کے بعد بھی نجات نہیں ملی، آزادی نے جنگ آزادی سے بھی زیادہ مشکل اور پیچیدہ مسائل پیدا کردیے تھے، ایک طرف فرقہ پروری کا سیلاب تھا جو آزادی کے اصل مقصد ہی کو خس وخاشاک کی طرح بہائے لیے جارہا تھا، دوسری طرف مسلمانوں کے سنگین مسائل تھے، تیسری جانب ملکی و وطنی مصالح اور صحیح جمہوری اور سیکولر بنیادوں پر آزاد ہندوستان کی تعمیر تھی، اس بحرانی دور میں ان سب سے عہدہ برآ ہونا آسان نہ تھا، فرقہ پروری نے بڑے بڑے قوم...

Pengaruh Komitmen dan Lingkungan Kerja Terhadap Produktivitas Kerja Karyawan Pada Paper Machine 6 PT. Indah Kiat Perawang

Penelitian ini bertujuan untuk mengetahui pengaruh komitmen dan lingkungan kerja terhadap produktivitas kerja karyawan pada Paper Machine 6 PT Indah Kiat Perawang.Populasi sebanyak 80 karyawan dan sekaligus menjadi responden. Data yang digunakan dalam penelitian ini adalah data primer dan alat analisis yang digunakan dalam penelitian ini adalah analisis regresi linear berganda dengan produktivitas kerja sebagai variabel dependen dan dua variabel independen yaitu variabel komitmen dan lingkungan kerja.Hasil penelitian ini menyatakan bahwa nilai koefisien determinasi sebesar 0,470, artinya hal ini menunjukkan bahwa Komitmen (X1) dan Lingkungan Kerja (X2) secara bersama-sama memberikan sumbangan terhadap Produtivitas Kerja sebesar 47%, dan sisanya (53%) dipengaruhi oleh faktor-faktor lain yang tidak terdapat dalam penelitian.

Characterization of Fungal Pathogen S Causing Wilt of Lentil and Their Management

Vascular wilt of lentil caused by various ecologically and phylogenetically diverse species of Fusarium is found in all the lentil growing areas of Pakistan and the disease could be visualized at both seedling and adult stages of plant growth. The disease is responsible for huge losses each year in Pakistan, yet, there is a scarcity and lack of literature and information regarding its occurrence, incidence, distribution, biology and management of wilt pathogens. Therefore, the study was planned keeping in view the national interests to avoid future losses caused by lentil wilt. The objectives of this study were to assess the wilt prevalence and incidence in major lentil growing districts of Punjab, morpho-molecular and pathogenic characterization of recovered wilt pathogens and the management through host plant resistance, biological control agents and fungicides. A two year field survey data (2011-12 and 2012-13) and laboratory isolations ascertained 213 isolates of Fusarium pathogen as associated wilt incidence identified in the fields. Disease was found widespread with 100% prevalence in all the major lentil growing districts of Punjab viz. Bhakkar, Layyah, Mianwali, Khushab, Sialkot, Narowal, Chakwal, Attock, Gujrat and Jhelum. The mean wilt incidence was found 28% with maximum incidence recorded at adult plant stage (32.4%) than at seedling (23.05%). Morphological characterization showed significant variation among the isolates and based on similar morphology, these were grouped into 67 type isolates for subsequent study. The in vitro pathogenicity testing through root dip method using line NARC-08-1 and cultivar Masoor-93 showed excellent production of wilt symptoms for pathogenic characterization. High pathogenic variability was revealed among the isolates. Based on disease reaction i.e. avirulent to highly virulent observed on most susceptible line NARC-08-1, isolates showed 0 to 100% disease incidence and severity index with significant (11.86 to 100%) reduction in yield. The isolates were grouped into four categories viz. highly virulent (13 isolates, 19.40%), moderately virulent (41, 61.19%), low virulent (8, 11.94%) and avirulent (5, 7.46%). The highly virulent isolates included FWC15, FWJ35, FWJ49, FWG1, FWS11, FWS13, FWN2, FWL2, FWL6, FWL9, FWL12, FWB10 and FWK2. Molecular characterization and DNA sequencing of isolates through PCR amplification of translation elongation factor TEF-1α gene region using primers ef1 and ef2 confirmed the identity of the Fusarium isolates at species level. The amplification produced a single DNA fragment of size 700bp in each of the isolates. Phylogenetic analysis of 67 morphologically and pathogenically diverse Fusarium isolates recovered from various lentil districts of the country revealed that the isolates belonged to different clades under five distinct species. The identified species included F. oxysporum, F. redolens, F. nygamai, F. commune and F. equiseti. This data supported the morphological variation observed among the isolates and divulged the association of these identified species in wilt disease incidence as reported in the major lentil producing region of the country. The findings revealed the highest prevalence of F. oxysporum (49.29%) in the region followed by F. redolens (29.57%), F. equiseti (10.79%) and F. commune (7.98%), while least prevalence was of F. nygamai (2.34%). The most virulent F. oxysporum isolate FWL12 (GenBank accession number KP297995) was selected for the management trials. Screening of the lentil germplasm revealed reduced wilt infection in five cultivars viz. Markaz-09, Masoor-86, Masoor-2006, Punjab Masoor-00518, Punjab Masoor-09 that showed 4.44 to 12.59% severity index, 20 to 46.67% incidence and 9.60 to 24.94% yield reduction. The biological management revealed the best efficiency of T. harzianum in reducing wilt infection on line NARC-08-1 and produced 8.9% disease severity index, 26.7% incidence with 16.27% yield reduction. Chemical seed treatment identified systemic fungicides as highly effective in disease management that resulted in improved 100% seed germination. Benomyl (6.7% incidence and 1.5% severity index) was found superior than Thiophanate methyl (13.3%, 3%). In conclusion, the results of this research study provide an overall current status of wilt disease in the country and high lightened the areas under current high risk of its spread. The findings also revealed the continuous reduction in the acreage of this crop in the major lentil region. The revealed association of five virulent and morpho-molecularly diverse species viz. F. oxysporum, F. redolens, F. nygamai, F. commune and F. equiseti with the wilt disease is reported for the first time in Pakistan. The screening suggests five cultivars viz. Markaz-09, Masoor-86, Masoor-2006, Punjab Masoor-00518 and Punjab Masoor-09 as an important source of resistance for lentil breeding against wilt. Moreover, T. harzianum proves an efficient biological control agent, while seed treatment suggests Benomyl and Thiophanate methyl as the most effective against the wilt pathogen.