Commenced in January 2007
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Edition: International
Paper Count: 2

Search results for: Md Abu Saieed

2 Improvement a Lower Bound of Energy for Some Family of Graphs, Related to Determinant of Adjacency Matrix

Authors: Saieed Akbari, Yousef Bagheri, Amir Hossein Ghodrati, Sima Saadat Akhtar

Abstract:

Let G be a simple graph with the vertex set V (G) and with the adjacency matrix A (G). The energy E (G) of G is defined to be the sum of the absolute values of all eigenvalues of A (G). Also let n and m be number of edges and vertices of the graph respectively. A regular graph is a graph where each vertex has the same number of neighbours. Given a graph G, its line graph L(G) is a graph such that each vertex of L(G) represents an edge of G; and two vertices of L(G) are adjacent if and only if their corresponding edges share a common endpoint in G. In this paper we show that for every regular graphs and also for every line graphs such that (G) 3 we have, E(G) 2nm + n 1. Also at the other part of the paper we prove that 2 (G) E(G) for an arbitrary graph G.

Keywords: eigenvalues, energy, line graphs, matching number

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1 Mechanisms and Process of an Effective Public Policy Formulation in Islamic Economic System

Authors: Md Abu Saieed

Abstract:

Crafting and implementing public policy is one of the indispensable works in any form of state and government. But the policy objectives, methods of formulation and tools of implementation might be different based on the ideological nature, historical legacy, structure and capacity of administration and management and other push and factors. Public policy in Islamic economic system needs to be based on the key guidelines of divine scriptures along with other sources of sharia’h. As a representative of Allah (SWT), the governor and other apparatus of the state will formulate and implement public policies which will enable to establish a true welfare state based on justice, equity and equality. The whole life of Prophet Muhammad (pbuh) and his policy in operating state of affairs in Madina is the practical guidelines for the policy actors and professionals in Islamic system of economics. Moreover, policy makers need to be more meticulous in formulating Islamic public policy which meets the needs and demands of contemporary worlds as well.

Keywords: formulation, Islam, public policy, policy factors, Sharia’h

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