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In this article, we study the signed distance matrix of the product of signed graphs such as the Cartesian product and the lexicographic product in terms of the signed distance matrices of the factor graphs. Also, we discuss the distance spectra of some special classes of product of signed graphs. [ABSTRACT FROM AUTHOR]

A signed graph is an ordered pair Σ = (G,σ), where G = (V, E) is the underlying graph of Σ with a signature function σ : E → {1, -1}. In this article, we define the nth power of a signed graph and discuss some properties of these powers of signed graphs. As we can define two types of signed graphs as the power of a signed graph, necessary and sufficient conditions are given for an nth power of a signed graph to be unique. Also, we characterize balanced power signed graphs. [ABSTRACT FROM AUTHOR]