ABSTRACT
This chapter surveys the research conducted on algebraic graphs, with a focus on the odyssey of algebraic signed graphs associated with a finite commutative ring. In particular, it also focuses on the problems which are based on balanceness and consistency of algebraic signed graphs. The chapter discusses the interplay between ring-theoretic and graph theoretic properties. There are three problems in the study of algebraic graphs: characterization of the resulting algebraic graphs; characterization of the algebraic structures with isomorphic graphs; and realization of the connections between the structures and the corresponding graphs. The Zero-divisor graph, Cayley graph, Total graph, Zero ring graph, Co-maximal graph are the examples of an algebraic graph. The chapter also discusses the criteria for sign-compatibility, existing algebraic signed graphs, signed total graphs, balanced signed total graphs, and the signed unit graphs.
