Additive compound graphs Original Research Article

Based on matrix theory notions, we assign to an undirected finite (in general, signed) graph G on n vertices and each integer k, 1 ⩽ k ⩽ n, the kth additive compound graph G[k]. This is again an undirected signed graph on image vertices. We investigate the basic properties of these graphs, e.g. show that they preserve connectedness of G, prove that the path Pn is the only connected graph G with all edges positive for which G[2] has only positive edges. The corresponding graphs Pn[k] as well as their spectral properties are completely described.