The minimum number of complete bipartite subgraphs needed to partition the edges of a graph G is denoted by b(G). A known lower bound on b(G) states that \(b(G)\ge r(G)= \max \{p(G), q(G)\}\) , where p(G) and q(G) are the numbers of positive and negative eigenvalues of the adjacency matrix of G, respectively. Graphs satisfying \(b(G) = r(G)\) (or \(b(G) = r(G)+1\) ) are called eigensharp and almost eigensharp, respectively. In this paper, we investigate the eigensharpness and almost eigensharpness of semistrong product of some graphs, grid graphs and cubic Cayley graphs over cyclic and dihedral groups.
