A difference labeling of a graph G is an injective function f: V (G) → N ∪ {0} together with the weight function f∗ on E(G) given by f∗(uv) = |f(u)-f(v)| for every edge uv in G. The collection of subgraphs induced by the edges of the same weight is a decomposition of G and is called the common weight decomposition of G induced by f. Let ϒf denote the collection of all the paths taken from each member of the common weight decomposition induced by f. A difference labeling f of G is said to be a Graphoidal difference labeling if ϒf is an acyclic Graphoidal decomposition of G. This paper initiates a study on this concepts.

Let G=(V, E) be a graph with p vertices and q edges. An acyclic Graphoidal cover of G is a collection y of paths in G which are internally-disjoint and cover each edge of the graph exactly once. Let f:V® {1, 2, …, P} be a bijective labeling of the vertices of G. Let ­Gf be the directed graph obtained by orienting the edgesuv of G from u to v provided f(u)<f(v). If the set yf of all maximal directed paths in ­Gf, with directions ignored, is an acyclic Graphoidal cover of G, then f is called a Graphoidal labeling of G and G is called a label Graphoidal graph and  hi=min {½yf½: f is a Graphoidal labeling of G} is called the label Graphoidal covering number of G. In this paper we characterize graphs for which (i) hi=q-m, where m is the number of vertices of degree 2 and (ii) hi=q. Also, we determine the value of label Graphoidal covering number for unicyclic graphs.

In this paper, we investigate the pair difference cordial labeling behaviour of some star related graphs.

In this paper we investigate the pair difference cordial labeling behavior of double alternate triangular snake and double alternate quadrilatral snake graphs.

A double ambiguity has been charged against Rawls’s difference principle (DP). Is it Maximin, Leximin, or something else? Usually, following A. Sen, scholars identify DP with the so-called Leximin. One argues here that one has to distinguish 1° the Leximin, 2° the Maximin (as rule of justice formally analogous to the maximin rule of decision), represented by the figure in L of the perfectly substitutable goods, and 3° the genuine DP. When the augmentation of inequality benefits the worse off, only Pareto-strong improvements are permitted. Leximin would also permit Pareto-weak improvements too (after the first maximum D), where only the richest improves: from (2, 3) to (2, 5), say. This is forbidden by DP. With two classes, unlike Maximin, DP has no curve of indifference and is always decisive, as Leximin is. For undecisive Rules of Justice, which admit indifferent curves, I propose to add a lexically secondary rule, to break ties. That move is able to clarify the links and the differences between on the one hand Maximin alone, with its typical indifference curves in L, and on the other hand, the DP properly understood and the Leximin, which both have no indifferent curves. With two classes of persons (best off/worse off), DP appears more egalitarian than Leximin, because it's secondary rule is MinIn (Minimization of Inequality). But the intuition behind the distinction is that it cannot possible “fair” that only the best off improves in a productive social cooperation.

Let G be a graph and f: V (G)! {1, 2, 3, . . . . . |V (G)|} be a bijection. Let puv = f(u)f(v) and duv =        hf(u) f(v) i if f(u)  f(v) hf(v) f(u)i if f(v)  f(u) for all edge uv 2 E(G). For each edge uv assign the label 1 if gcd(puv, duv) = 1 or 0 otherwise. f is called PD-prime cordial labeling if |ef (0) − ef (1)|  1 where ef (0) and ef (1) respectively denote the number of edges labelled with 0 and 1. A graph with admit a PD-prime cordial labeling is called PD-prime cordial graph.

Relation between religion and sociological theories is the most important concern of scholars who study in the field of social sciences.Different views have been expressed in this regard. To draw them on a line one must put on one side those views which reject the existence of any relation between them. On the other side those who believe that faith can take part in this area. Islam as a complete religion has solutions both for spiritual guidance of man and for man’s social life. We should just discover these solutions. New theories such as sociological theories guide us to discover these laws.The present paper lies at the middle of this line between two sides of it. The author has a middle approach. He starts his research with a little question in the field of sociology namely social-labeling theory and then explores different aspects of this theory and highlights its most important points and finally makes a comparison between them and hadith sources trying to find an answer.