Czerwi’nski et al. introduced Lucky labeling in 2009 and Akbari et al and A.Nellai Murugan et al studied it further. Czerwi’nski defined Lucky Number of graph as follows: A labeling of vertices of a graph G is called a Lucky labeling if  for every pair of adjacent vertices u and v in G where . A graph G may admit any number of lucky labelings. The least integer k for which a graph G has a lucky labeling from the set 1, 2, k is the lucky number of G denoted by η(G). This paper aims to determine the lucky number of Complete graph K_n, Complete bipartite graph K_m,n and Complete tripartite graph K_l,m,n. It has also been studied how the lucky number changes whi

Throughout this paper R represents commutative ring with identity and M is a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of weak essential submodules which introduced by Muna A. Ahmed, where a submodule N of an R-module M is called weak essential, if N ? P ? (0) for each nonzero semiprime submodule P of M. In this paper we rewrite this definition in another formula. Some new definitions are introduced and various properties of weak essential submodules are considered.

Throughout this paper R represents commutative ring with identity and M is a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of weak essential submodules which introduced by Muna A. Ahmed, where a submodule N of an R-module M is called weak essential, if N ? P ? (0) for each nonzero semiprime submodule P of M. In this paper we rewrite this definition in another formula. Some new definitions are introduced and various properties of weak essential submodules are considered.

In this work, we study several features of the non-zero divisor graphs (ℵZD- graph) for the ring Zn of integer modulo n. For instance, the clique number, radius, girth, domination number, and the local clustering coefficient are determined. Furthermore, we present an algorithm that calculates the clique number and draws the non-zero divisor for the ring Zn.

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

THE EFFECT OF SPREACL of KNOWLEDGE ON ETHICS