Islam is the Religion of Peace: Analytical Review from the Life of Holy Prophet PBUH

Islam is the religion of peace and mercy for all creatures. But, now-adays, some extremist has spread misconception about the Islam, that as, it is the religion of sword for terror. But, the actual fact is that, Islam is the religion of peace and it condemns extremism and violence. Islam promotes the peace, calm, harmony, any tranquility in society. Islam is a peaceful religion, its best examples, we can see, in the practical life of Holy Prophet (SAW). He was the Messenger of Allah (SWT) to convey the message of honesty, piousness, peace, mercy, integrity, and love. He had never done any activity which indicate act of terrorizing, misconduct, racism and violation against humanity. Even though, he showed the mercy on animals, insects and plants. The world knows him, as a 'Rahmatul-lil-Aālamyn'(Mercy into the world). From the life of Holy Prophet (SAW), it is concluded that Islam is the religion of peace and humanity. It did not spread by the forced of sword, rather, it spread by its golden quality. 

Properties of Graphs With H-Covering and Prescribed H-Weights

Let vertex and edge sets of graph G are denoted by V (G) and E(G), respectively. An edge-covering of G is a family of di erent subgraphs H1;H2; : : : ;Hk such that each edge of E(G) belongs to at least one of the subgraphs Hj , 1 j k. Then it is said that G admits an (H1;H2; : : : ;Hk)-(edge)covering. If every Hj is isomorphic to a given graph H, then G admits an H-covering. For axed graph H, a total labeling : V (G) [ E(G) ! f1; 2; : : : ; jV (G)j + jE(G)jg is said to be H-magic if all subgraphs of G isomorphic to H have the same weight. One can ask for di erent properties of a total labeling. The total labeling is said to be antimagic if the weights of subgraphs isomorphic to H are pairwise distinct. Further restriction on the weights of subgraphs provides (a; d)-H-antimagic labelings where the weights of subgraphs form an arithmetic progression with di erence d and rst element a. If graph G is a 2-connected plane graph then the H-antimagic labeling is equiva- lent to d-antimagic labeling of type (1; 1; 0), where weights of all faces form an arith- metic sequence having a common di erence d and the weight of a face under a labeling of type (1; 1; 0) is the sum of labels carried by the edges and vertices on its boundary. In therst part of the thesis we will study the notions, notations and de nitions about graphs and labeling of graphs. In the second part of the thesis, we have three chapters on newly obtained results. In the chapters, we examine the existence of Hk 2 -supermagic labelings for graphs Gk 2 obtained from two isomorphic graphs G and G0 by joining every couple of corre- sponding vertices v 2 V (G) and v0 2 V (G0) by a path of length k + 1. We show that graphs Gk(w), obtained from a graph G by joining all vertices in G to a vertex w by paths of length k + 1, keep super H-antimagic properties of the graph G. We also examine the existence of the (H G2)-supermagic labelings of Cartesian product G1 G2, where G1 admits an H-covering and G2 is a graph of even order. Addition- ally, we show that if a graph G admits a (super) (a; 1)-tree-antimagic labeling then the disjoint union of multiple copies of the graph G keeps the same property.