مغربی اور اسلامی نظریہ ثقافتی اور تہذیبی عالمگیریت تحقیقی جائزہ

The term globalization is not new to the modern world. It was a hope of humanity centuries ago to make the planate a global village. However there is a difference of interests of nations in doing so. In the present ages the word Globalization is considered as a tool and term used by western powers to rule the entire world. If we see the globalization from Islamic perspective we can find various contracatidions between the concepts of Islam and that of the western world about globalization. These differences are not limited to a single side of globalization, but are found in political, financial and cultural point of views as well. In this paper I have limited my topic to cultural globalization, where after a brief study of both terms I have come up with an analysis of both, their modern status and current situation. This paper consists of a detailed comparision of both concepts from different dimentions and their impact on human society.

Multilevel and Antipodal Labelings for Families of Graphs

A radio k-labeling c of a graph G is a mapping c : V (G) → Z+ ∪ {0}, such that d(x, y) + |c(x) − c(y)| ≥ k + 1 holds for every two distinct vertices x and y of G, where d(x, y) is the distance between any two vertices x and y of G. The span of a radio k-labeling c is denoted by sp(c) and defined as max{|c(x) − c(y)| : x, y ∈ V (G)}. The radio labeling is a radio klabeling when k = diam(G). In other words, a radio labeling is a one-to-one function c : V (G) → Z+ ∪ {0}, such that |c(x) − c(y)| ≥ diam(G) + 1 − d(x, y) for any pair of vertices x, y in G. The radio number of G denoted by rn(G), is the lowest span taken over all radio labelings of the graph. When k = diam(G) − 1, a radio klabeling is called a radio antipodal labeling. An antipodal labeling for a graph G is a function c : V (G) → {0, 1, 2, ...}, so that d(x, y) + |c(x) − c(y)| ≥ diam(G) for all x, y ∈ G. The radio antipodal number for G denoted by an(G), is the minimum span of an antipodal labeling admitted by G. In this thesis, we investigate the exact value of the radio number and radio antipodal number for different family of graphs. Further more, we also determine the lower bound of the radio number for some cases.