This monograph is an embarkation of constructing new algebraic structures from old ones together with some graph theoretic aspects.The essence begins with construction of new groups and near-rings from given two such as in the cases through direct sums and direct products leading for an exposition on what is discussed as wreath products and wreath sums and a fair number of algebraist have considerably contributed a lot so as to satisfy their respective needs.Following it, the author tries to incorporate the concept of wreath sums of near-ring groups together with its Noetherian and Goldie characters with examples wherever necessary.The rest part is devoted to give some exposition on the possible scope of graph theoretic aspects of associated algebraic structures.

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