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Some Vertex-Degree-Based Topological Indices of Graphs

Thesis Info

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Author

Akbar Ali

Program

PhD

Institute

National University of Computer and Emerging Sciences

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2016

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/2887/1/akbar.ali.phd.thesis.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727211053

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Many topological indices which are being used by researchers in the quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies to predict the physico-chemical properties of molecules, are based on vertex degrees of the corresponding molecular graphs. When a new topological index is introduced in chemical graph theory, one of the important questions that need to be answered is for which members of a certain class of n-vertex graphs this index assumes minimal and maximal values? On the other hand, there are many well known graph families and vertex-degree-based topological indices in the literature for which this question remains open. The main purpose of current study is to address this open question for some well known families of graphs. Firstly, the collection of all k-polygonal chains (for k = 3, 4, 5) with fixed number of k-polygons is considered and the extremal elements from this family are characterized with respect to several well known bond incident degree (BID) indices (BID indices form a subclass of the class of all vertex-degree-based topological indices). From the derived results, many already reported results are obtained as corollaries. Furthermore, the extremal 4-polygonal (polyomino) chains for some renowned vertex-degree-based topological indices (other than BID indices) are also determined. Next, the problem of characterizing the extremal cacti over the certain classes of cacti (tree-like polyphenylene systems, spiro hexagonal systems and general cacti) with some fixed parameters is addressed for various well known vertex-degree-based topological indices. Finally, some mathematical properties of the atom-bond connectivity index and augmented Zagreb index are explored
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مولانا سعید احمد اکبر آبادی

مولانا سعیداحمد اکبرآبادی
اس سے زیادہ دلدوز خبر،مفتی عتیق الرحمن ؒ کے وصال کے بعد ندوۃ المصنفین ماہنامہ برہان کے لیے کوئی دوسری نہیں کہ ۲۴؍ مئی مولانا سعید اکبرآبادی کاکراچی میں انتقال ہوگیا۔اِنَّا لِلّٰہِ وَاِنَّا اِلَیْہِ رَاجِعُوْنَ ْ
مولانا سعید احمد اکبرآبادی کی رحلت،علمی، ادبی، اوردینی، اور صحافتی دنیا کا ایک ایسا نقصان ہے جس کی تلافی کی کوئی صورت بظاہر موجود نہیں ہے وہ ان نادر شخصیتوں میں سے جن کے اندر قدیم اورجدید علوم جمع ہوجاتے ہیں اور وہ زمانہ کو اپنی خداداد ذہانت اور طبائع کی روشنی سے منّور کرنے کاایسا عظیم الشان کام انجام دیتے ہیں، جوقدیم علوم کے ماہرین اور جدید علوم کے علمبردار وں سے الگ الگ صورت میں ممکن نہیں۔ مولانا سعید احمد اکبرآبادی ایک طرف علامہ انور شاہ کشمیریؒ کے ذریعہ اورواسطے سے ،اس سلسلۃ الذہب سے منسلک نظرآتے ہیں،جواسرار علوم نبوت کے محرموں اورفقہ وحدیث کے بالغ نظر عالموں، اسلامی شرع اوردینی کمالات کے حامل شخصیتوں کاایک ایسا قافلہ ہے، جس نے دینی علوم کوتحقیقی صلاحیتوں کے قالب میں ڈھال کر ہرزمانہ اور ہرعہد کے مطابق بنانے اور اس کی رہنمایانہ استعدادقائم ر کھنے میں ناقابلِ فراموش حصّہ لیا۔ دوسری طرف سے وہ جدید علوم سے پوری طرح واقف، اور دنیا میں سائنسی اورصنعتی اورمعاشی انقلابات کے اثرات ونتائج سے مکمل طورپر باخبر اور نئے زمانے کے تقاضوں کاپورا شعور رکھنے والے ایک دانشور تھے، جوقدیم علوم کی آب و تاب،مذہبی روایات کے تقدس کی برقراری اور اصول واحکام دین کی پاسداری بلکہ نگہبانی کافرض آدھی صدی سے بھی زیادہ مدّت تک انجام دیتے رہے۔وہ ایک طرف مفتی عتیق الرحمن عثمانی ؒ،مولانا حفظ الرحمن سیوہاروی ؒ، مولانامحمد یوسف بنوری ؒ، مفتی محمد شفیع دیوبندیؒ،قاضی زین العابدین سجاد میرٹھی(تعالیٰ اﷲ عمرہٗ) مولانا احمدعلی لاہوریؒ،اورمولانا قاری محمد طےّب قاسمیؒ ،جیسے نابغۃ العصراور فقید المثال ماہرین علوم شریعت اور...

آخرت سے متعلق ”ترجمان القرآن“ کے کلامی مباحث کا تجزیاتی مطالعہ

In this universe, if we look at the arrival of a human being, it will open up to us the secret that man did not come in this world suddenly, but he had gone through several worlds before stepping into this universe. The First World is called spiritual world where his soul was present and the argument is that when the soul enters the body of the baby and he starts to move in the womb of the mother, so the question now arises where was that soul before it entered the baby’s body? And where did that soul come from? Where it was and wherever it came from, the name of that universe is Spiritual world. After the spiritual world, there is a second world in the womb of the mother. In this world a man must live for at least nine months. Stop for a minute to see this amazing system of power that a baby remains alive in a moving grave for at least nine months. The object is to say that if a human being has to go through two worlds before coming into the universe, so if a fourth world is accepted after this world, what is the rational prohibition behind it? The life in the fourth world is called the life of Hereafter. If there is any disagreement with this name then let’s another name, but a fourth world still have to believe, because when the soul comes out of body after death, the same question will arise here that where did the soul go? In this article, it is examined that how author of “Tarjuman al-Qur’an” Abul Kalam Azad has proved the reality of life of Hereafter and what kind of arguments have given as an evidence in this tafsir?

Production of Biodiesel Analysis and Testing the Performance of Biodiesel Engine by Using Indigenous Resources

This study aims to find out the potential of three different non-edible feedstocks namely Jatropha, Castor and Linseed for biodiesel production. The mechanical expeller was used for oil extraction in Biofuel Laboratory, Energy & Environment Engineering Department, QUEST Nawabshah.The transesterification process was used to produce biodiesel with homogenous catalyst (Sodium hydroxide and Potassium hydroxide).The physcio-chemical properties such as kinematic viscosity, flash point, cetane number and density, Free fatty acids, Sulphur contents, Pour point, Total acid, Cloud point, Water content and Calorific value of crude oil and biodiesel were determined before and after production of biodiesel followed by ASTM standard methods. The Gas Chromatography-Mass Spectrometry Model Agilent 5975 GC-MSD was used for determination of fatty acid composition. The IUPAC method was applied for preparation of methyl esters of free fatty acids. The blends were prepared with 90%, 80% and 70% of petro diesel and 10%, 20% and 30% of biodiesel. These blends were designated as JB10, JB20 and JB 30 for Jatropha, CB10, CB20 and CB30 for Castor, and LB10, LB20 and LB 30 for Linseed respectively. After examining the characteristics of blended biodiesel samples, these were used in Internal Combustion (I.C) Engine for performance analysis and emission level. The results revealed that diesel oil has lower thermal efficiency as compared to all biodiesel blends. Out of all blends, JB10 showed higher efficiency with 22.32% and JB20 lower with 16.83% thermal efficiency as compared to 15.94% of D-100. However, almost same thermal efficiency of 19.5, 19.6, 19.0%, was found from 30% blends of JB, CB and LB respectively. It was discovered from the analysis that Jatropha blend of 10% (JB10) was more useful for achieving higher thermal efficiency in I.C. Engine. Moreover, the NOx concentration found by Chauhan was 2200 ppm, 2500 & 2700 for JB10, JB20 & JB30 respectively, whereas in this research work the NOx concentration was found in the range of 25-39 ppm in all blends of Jatropha. Based on overall thermal efficiency, particulates and gases emissions, 30% blends of Jatropha, Castor as well as Linseed may be recommended for utilization in I.C. Engines. This study also revealed that if 30% diesel oil is replaced with blended biodiesel of non-edible oils, then an amount upto Rs.138.6 Billion could be saved at national level.