Certain differential subordination implications for multivalent functions defined on the unit disc [Formula: see text] and meromorphic multivalent functions on the punctured unit disc [Formula: see text] are established. The results obtained generalize several earlier known results on differential inequalities.

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The study on graphs emerging from different algebraic structures like groups, rings, fields, vector spaces, etc. is a prominent area of research in mathematics, as algebra and graph theory are two mathematical fields that focuses on creating and analysing structures. There are numerous studies linking algebraic structures and graphs, which began with the introduction of Cayley graphs of groups. Several algebraic graphs have been defined on rings, which have huge-growing literature. In this article, we systematically review the literature on some variants of Cayley graphs that are defined on rings, to understand the research in this area.