اسلامی مملکت کے بین الاقوامی تعلقات عصرحاضر کے تناظر میں

Islam where considers the superiority of law, provision of justice and equity, building and purification of civilization and emphasis on the welfare of society, there ensures the first priority to humanity, peace and prosperity in the external relations. Islamic state keeps relations on the basis of equality with the world and non-Muslim citizens living within the state. On this belief and ideology Islam invites the world to set together. Islam on these principles of Islamic ideology and belief sets the foundation of collectiveness. On this principle the whole philosophy of life and living system are embraced, and the same Islamic law is the foundation of nations, on this behalf the Islamic state organized the relation with other states. In this way Islamic state on these principles keep relations with other states and within the state relations between Muslim and non-Muslim citizens on the basis of brotherhoods, equality, mercy and the principles of dignity of human being. Along with peace Islam set the principles of war which comprise ethical and prison limitations, duties and ethics amongst warrior, difference between the rights of fighters and non-fighters, treatment with pact holders and prisoners, and specified the way of better treatment with the defeated nations. He thought the manners of war to bloody man who consider everything right during the war. Islam lays great stress on equality, social justice, brotherhood and peace not only in state but across the boarders too. In this article a deep study is done to explain the relations of an Islamic state with other states. Islamic foreign policy emphasizes on the principles of equality among all the human beings and all the races and nations. Islam builds international relation on humanitarian basis.

On Metric Dimension of Some Families of Graph

For a connected graph G the distance d(u;v) between two vertices u;v 2V(G) is the length of the shortest path between them. A vertex w of a graph G is said to resolve two vertices u and v of G if d(w;u) 6= d(w;v). Let W = fw1;w2; ::::;wkg be an ordered set of vertices of G and let v be a vertex of G. The representation of a vertex v with respect to W denoted by r(vjW) is the k-tuple (d(v;w1);d(v;w2); :::;d(v;wk)). If distinct vertices of G have distinct representations with respect toW, thenW is called a resolving set for G. The metric dimension of G denoted by dim(G), is the minimum cardinality of a resolving set of G. Graph structure can be used to study the various concepts of Navigation in space. A work place can be denoted as vertex in the graph, and edges denote the connections between the places. The problem of minimum machines (or Robots) to be placed at certain vertices to trace each and every vertex exactly once is a classical one. This problem can be solved by using networks where places are interconnected in which, the navigating agent moves from one vertex to another in the network. The places or vertices of a network where we place the machines (robots) are called landmarks. The minimum number of machines required to locate each and every vertex of the network is termed the metric dimension and the set of all minimum possible number of landmarks constitute metric basis. In this thesis, the metric dimension of some well known families of graphs has been investigated. It is shown that the families of graphs obtained from the path graph by the power, middle and total graph operation have a constant metric dimension. We compute the metric dimension of some rotationally symmetric families of graphs and show that only 2 or 3 vertices appropriately chosen suffice to resolve all the vertices of these graphs. In this thesis, we also compute the metric dimension of some families of convex polytopes with pendant edges. It is shown that the metric dimension of these families of graphs is constant and is independent of the order of these graphs. The metric dimension of the splitting graphs of two families of graph has been computed. We prove that the metric dimension of these graphs is unbounded and depends on the order of the corresponding graph.