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On the Topological Properties of Suduko Graph

Thesis Info

Author

Khadim Hussain

Supervisor

Muhammad Javaid

Program

Mphil

Institute

Riphah International University

Institute Type

Private

Campus Location

Faisalabad Campus

City

Faisalabad

Province

Punjab

Country

Pakistan

Thesis Completing Year

2018

Thesis Completion Status

Completed

Page

v, 43 . : ill. ; 30 cm.

Subject

Mathematics

Language

English

Other

Submitted in fulfillment of the requirements for the degree of M.Phil in Mathematics to the Faculty of Basic Sciences.; Includes bibliographical references; Thesis (M.Phil)--Riphah International University, 2018; English; Call No: 515.73 KHA

Added

2021-02-17 19:49:13

Modified

2023-02-19 12:33:56

ARI ID

1676711293068

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ان سطروں کے لکھتے وقت مولانا سید ابوالحسن علی ندوی کے عزیز بھانجے جناب محمد ثانی حسنی کی وفات حسرت آیات کی اندوہناک خبر ملی، ان کو مولانا علی میاں اپنے فرزند کے برابر سمجھتے رہے، وہ اپنی متانت ، سنجیدگی اور خاموشی کی وجہ سے اپنے حلقہ میں بڑی قدر کی نظر سے دیکھے جاتے تھے، بڑے اچھے اہل قلم بھی تھے، ان کی کتابوں میں ایمانی حرارت و حمیت جلوہ گر رہتی تھی، ان کی وفات سے دارالمصنفین بھی سوگوار ہے، اس لیے بھی کہ یہاں جو سیمینار ہورہا ہے اس کے روح رواں مولانا علی میاں اور ان کے دست و بازو مولانا رابع ندوی تھے، جو مرحوم کے منجھلے بھائی تھے، ان کی سوگواری سے ہمارے سیمینار کی فضا بھی غم ناک رہے گی، دعا ہے کہ مرحوم کو کروٹ کروٹ جنت نعیم اور ان کے سوگوارماموں، بھائیوں اور بچوں کو صبر جمیل عطا ہو۔ (صباح الدین عبدالرحمن، فروری ۱۹۸۲ء)

 

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Biosystematics of Wasps Species Hymenoptera: Vespidae from Hazara Region, Khyber Pakhtunkhwa, Pakistan

Present study describes the phylogenetic reconstruction of wasp species found in the Hazara region of Northern Pakistan. The investigation was based on morphological characteristics and nucleotide sequence analysis of specific markers which have been extensively used for the phylogenetic studies including: 12S rRNA, 16S rRNA, 28S rRNA, Co1, Cyt-B, Jerry, Wg and Pol genes. Morphological identification of 4500 samples was carried out which represented nineteen (19) species from three (3) sabfamilies incuding: Eumeninae: six species, Polistinae: six species and subfamily Vespinae: seven species. Among the identified samples, nine species: Delta conoideum, D. esuriens, Anterhynchium abdominale bangalensis, Rhynchum qunquecinctum, Antodynours flavesens, Ropalidia brevita, P. olivaceous, P. stigma and V. mandarinia are new for Hazara region whereas four species: V. mandarinia, Anterhynchium abdominale bangalensis, Rhynchum qunquecinctum and Antodynours flavesens are new record from Pakistan. DNA based identification using 12S rRNA gene for subfamily Eumeninae A. a. bangalensis, R. quinquecintum, A. flavesens showing 89-86% homology, whereas D. dimidiatipenne 69% representing an out group. Species of subfamily Polistinae, P. indicus, P. wattii showing 100% homology, however P. rothneyi, P. stigma 91-86% but R. brevita 76% which is an out group. In subfamily Vespinae, V. mandarina, V. tropica showing 100% homology, Vespa analis and V. orientalis 91-90%. Using of 16S rRNA gene, A. a. bangalensis, A. flavesens, R. quinquecintum having the same group of Eumeninae species 90-89% homology, whereas D. conoideum and D. dimidiatipenne 88% and D. esuriens 57%, representing an out group. Members of subfamily P. indicus, P. wattii showing 99% homology, P. olivaceous and P. rothneyi 94% and Ropalidia brevita 86%. Species of subfamily Vespinae V. tropica and V. velutina showing 100% homology and V. analis 64%, whereas V. germanica 54%. On partial sequences of 28S rRNA gene, A. flavesens, R. quinquecintum showing 93% homology but A. a. bangalensis 64%. Subfamily Polistinae, P. indicus, P. olivaceous, Ropalidia brevita showing 97-89% homology and P. wattii 81%, which is an out group. However subfamily Vespinae include, V. germanica, V. velutina, V. orientalis showing 99-77% homology, but V. mandarina and V. tropic 79%. Homology based on partial sequences of COI gene, Delta conoideum and Delta dimidiatipenne showing 87% homology, whereas A. a. bangalensis, A. flavesens and R. qunquecinctum 83%, but Delta esuriens 63%, which is an out group in the subfamily of Eumeninae. In the subfamily Polistinae, P. indicus, P. wattii showing 100% of homology, whereas P. olivaceus, P. rothneyi and P. stigma 91-87%, but Ropalidia brevita 82%. However the species of subfamily Vespinae, V. mandarina, V. tropica, V. velutina showing 100% homology, whereas V. analis and V. orientalis 86%. Using of partial sequences of Cyt-B gene, D. conoideum, D. esuriens showing the same group 100% of homology, whereas A. a. bangalensis, D. dimidiatipenne 86% and A. flavesens, R. qunquecinctum 79%. In Polistinae species, P. indicus, P. wattii showing 100%, P. olivaceus, P. rothneyi 90-89%, whereas P. stigma 87%. Vespa mandarina, V. orientalis representing the same group 100% homology, whereas V. analis, V. basalis 84% and Vespa tropica 81% subfamily Vespinae. By using partial sequences of Jerry gene, species of the subfamily Eumeninae, D. conoideum, D. dimidiatipenne showing 90% homology and A. a. bangalensis, Rhynchium qunquecinctum, D. esuriens 89%, whereas A. flavesens 86%. Subfamily Polistinae, P. indicus, P. wattii showing homology of 100% and P. olivaceus, P. rothneyi, P. stigma 96%, whereas Ropalidia brevita 86%. Vespa mandarina, V. tropica showing 91% homology and V. analis, V. basalis, V. orientalis 90-89%, whereas V. germanica showing 86% in the subfamily Vespinae. Partial sequence Wg gene, resulting D. conoideum, D. dimidiatipenne 98% homology, whereas A. a. bangalensis, R. qunquecinctum, A. flavesens 95-92% and D. esuriens 82% of subfamily Eumeninae. Species of the subfamily Polistinae, P. indicus, P. wattii, P. rothneyi showing 100-98% homology and Ropalidia brevita 84%. Two species of subfamily Vespinae, V. analis, V. orientalis showing 99% homology, whereas V. basalis, Vespa mandarina and V. tropica 98%. With the use of partial sequence of Pol gene, species of the subfamily Eumeninae, A. a. bangalensis, R. qunquecinctum showing 96% homology, whereas D. conoideum 35% representing an out group. Members of the subfamily Polistinae, P. indicus, P. wattii, P. olivaceus showing 100% homology, whereas P. rothneyi, P. stigma 99% and Ropalidia brevita 95%, subfamily Vespinae, V. analis, V. orientalis 100%, whereas V. mandarina, V. tropica 99%. The results have shown that the taxonomic position of wasp species based on morphological charaters can be verified, further refined or modified by the use of modern molecular biological tools which involve the nucleotide sequence of genes used in phylogenetic investigations. It was concluded that 12S rRNA, 28S rRNA, COI and Wg shows the best result for identification and phylogenetic whereas 16S rRNA, Cyt-b, Pol and Jerry genes showing not good result during the current study. Moreover our study provides the first report for the phylogenetic reconstruction and cataloguing of wasp species found in Hazara Division, Pakistan.