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H- Magic Behaviors of Some Graphs

Thesis Info

Access Option

External Link

Author

Cheema, Imran Zulfiqar

Program

PhD

Institute

COMSATS University Islamabad

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2018

Thesis Completion Status

Completed

Subject

Statistics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/11281/1/Imran_Zulfiqar_Cheema_soft_copy_for_upload.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726353115

Similar


A graph ( , ) G V E has an H -covering if every edge in Ebelongs to a subgraph of G isomorphic to H . SupposeG admits an H -covering. AnH -magic labeling is a mapping l from ( ) ( ) E G V G È onto the integers {1,2,...,| ( ) ( )|} E G V G È with the property that, for every subgraph Aof G isomorphic toH , there is a positive integer csuch that ( ) ( ) ( ) ( ) . v V A e E A A v e c ll ÎÎ = å + å =å A graph which possess such type of labeling is known as H -magic graph. Further if in a graph vertices are labeled first with smallest positive numbers, then the graph is called H -supermagic. Moreover a graph is said to be H -( , ) ad-anti magic if the magic constant for an arithmetic progression with initial value aand a common difference . d Numerous results on labeling of many families of graphs have been published. In this thesis, research work focuses on to formulate cycle 3 C -( , ) ad anti-supermagic labeling for the MultiWheels graph, supermagic labeling for isomorphic copies with its disjoint union of Multi-Wheels graph and cycle ( , ) ad-anti-supermagic labeling for Web graph. Also cycle anti-supermagic labeling for isomorphic copies with its disjoint union of ladder and triangular ladder graphs have been formulated. In addition, investigation of fan, friendship, ladder and wheel line graphs and study of the supermagic and anti-supermagic vertex-edge-face labeling of such graphs and their isomorphic copies have been carried in this thesis. An anti-supermagic labeling of the extension of cycle graphs is also formulated.Lastly the face supermagic labeling of (1,1,1) type of subdivided triangular ladder graph, subdivided 4 mC -snake graph and subdivided 4 kmC -triangular snake graph with its (1,1,...,1) and (2,2,...,2) string are also the part of this thesis.
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مختلف اعضا ء کی دیت

حضرت ابو بکر بن محمد بن عمرو بن حزمؒ (م:120ھ)اپنے والد سے روایت کرتے ہیں کہ رسول اللہ ﷺ نے ان کو دیت کے بارےمیں تفصیلاً لکھا
"أَنَّ فِي النَّفْسِ مِائَةً مِنْ الْإِبِلِ وَفِي الْأَنْفِ إِذَا أُوعِيَ جَدْعًا مِائَةٌ مِنْ الْإِبِلِ وَفِي الْمَأْمُومَةِ ثُلُثُ الدِّيَةِ وَفِي الْجَائِفَةِ مِثْلُهَا وَفِي الْعَيْنِ خَمْسُونَ وَفِي الْيَدِ خَمْسُونَ وَفِي الرِّجْلِ خَمْسُونَ وَفِي كُلِّ أُصْبُعٍ مِمَّا هُنَالِكَ عَشْرٌ مِنْ الْإِبِلِ وَفِي السِّنِّ خَمْسٌ وَفِي الْمُوضِحَةِ خَمْسٌ۔"173
" جان کے بدلے میں سو اونٹ ہیں اور جب ناک مکمل کاٹ دی جائے تو سو اونٹ اور دماغ اور پیٹ کے زخم میں تہائی دیت ہے اور آنکھ کی دیت پچاس اونٹ اور ہاتھ اور پاؤں کی دیت میں پچاس اونٹ اور ہر انگلی میں اسی طرح دس اونٹ ہیں اور دانت اور موضحہ زخم میں پانچ پانچ اونٹ ہیں۔ "
حضرت ابو بکر بن محمد بن عمرو بن حزمؒ اپنے والد سے اور وہ اپنے دادا سے روایت کرتے ہیں کہ رسول اللہ ﷺ نے یمن کے باشندوں کے نام ایک خط لکھا ،جس کے الفاظ یہ تھے
" وَفِي الْأَنْفِ إِذَا أُوعِبَ جَدْعُهُ الدِّيَةُ وَفِي اللِّسَانِ الدِّيَةُ، وَفِي الشَّفَتَيْنِ الدِّيَةُ وَفِي الْبَيْضَتَيْنِ الدِّيَةُ، وَفِي الذَّكَرِ الدِّيَةُ وَفِي الصُّلْبِ الدِّيَةُ، وَفِي الْعَيْنَيْنِ الدِّيَةُ وَفِي الرِّجْلِ الْوَاحِدَةِ نِصْفُ الدِّيَةِ، وَفِي الْمَأْمُومَةِ ثُلُثُ الدِّيَةِ، وَفِي الْجَائِفَةِ ثُلُثُ الدِّيَةِ، وَفِي الْمُنَقِّلَةِ خَمْسَ عَشْرَةَ مِنَ الْإِبِلِ۔"174
"اگر کسی کی ناک پوری کاٹی جائے تو پورا خون بہا ہو گا۔ زبان کے کاٹے جانے پر بھی پوری دیت ہے۔ ہونٹوں پر بھی پوری دیت ہے۔ خصیوں پر بھی پوری دیت ہے ۔ آلہ تناسل پر بھی پوری دیت ہے ۔ پیٹھ کی ہڈی پر بھی پوری دیت ہے۔ آنکھوں پر بھی پوری دیت ہے ، ایک ٹانگ پر آدھی دیت ہے، آمہ (دماغ کا زخم)پرتہائی دیت ہے۔ زخمی کرنے پر بھی تہائی دیت ہے اور زخم سے...

الأسس الفلسفية لأسلوب الحياة الإسلامية وغير الإسلامية وأثرها فى المجتمع: دراسة مقارنة

Philosophical Foundations of Islamic and Un-Islamic Pattern of Life and its Impact upon Society: A Comparative Study It is self-evident that human beliefs had great influence on character, actions, ethics, behavior and way of life. The possessors of correct belief produced positive effects and those who possessed incorrect belief promoted negative values in the community. Undoubtedly, the diversity in belief produced diverse ethics, actions, behaviour which gave birth to the different patterns of life in society. Regardless of subdivisions, by looking towards the philosophical foundations, these patterns of life could be divided into four categories in the light of the Qur’an and Sunnah. These lifestyles (also mentioned by Abū ’l-A‘lā Maudūdī in Tajdīd wa Iḥyā-i Dīn) are: Atheistic pattern of life, Polytheistic pattern of life, Monastic pattern of life and Islamic pattern of life. As each pattern had its particular tenets, therefore it formed a particular way of life by leaving its effects upon individual, social, political, economic, cultural and civilizational life. This research work aimed to explain the basic mechanism of these four patterns and their impact on human life. The method used for the collection and analysis of data was descriptive and analytical. The research concluded that three patterns of life (except Islamic pattern of life) produced harmful and negative effects into the society whereas the only Islamic pattern of life ensured the peace and prosperity. Moreover, Islamic pattern of life played a vital role in growth of all disciplines including political social, and economic system. It is therefore suggested that Islamic scholars should uncover the hollowness of Un-Islamic life style and present Islamic pattern of life in logical and systematic way. On one hand, this exercise will encounter the evils and on the other hand would promote good into the society.

Study of Some Properties of Central Carbon- Carbon Collisions at 4. 2 a Gev/C

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