This is a preview. Log in through your library . Abstract This paper considers the planar decomposition of a complete bipartite graph, that is, the decomposition of a complete bipartite graph into ...

In this paper, we study the spectral radius of bipartite graphs. Let 𝐺 be a bipartite graph with 𝑒 edges without isolated vertices. It was known that the spectral radius of 𝐺 is at most the square ...

Let us say that a graph is k-apex if it contains a set of at most k vertices whose removal yields a planar graph. We define the apex number of a graph G as the minimum k for which G is k-apex. It is ...