Compatibility of the ????-Product of Signed Graphs

A signed graph is a graph whose edges are assigned to a sign, positive or negative, by a function E M El-Kholy et.al. defined the ????-product of two graphs and as the graph with vertex set and two vertices and are adjacent in if and only if is adjacent to in and ????2 is not adjacent to ????2 in ????2, or ????1 is not adjacent to ????1 in ????1 and ????2 is adjacent to ????2 in ????2. This paper discusses structural properties and connectivity of the ????-product of graphs. The ????-product of two signed graphs is the signed graph with the vertex set and edge set as that of the unsigned product and the sign of an edge in the ???? -product is determined by the sign of the adjacency in the component signed graphs. This work also examines the compatibility of ????-products for graph classes such as complete graphs and cycles.