The line graph of the complete bipartite graph on sets with m and n vertices, denoted by L (Bmn), is the graph with mn vertices given by all ordered pairs (i, j), 1 ≤ i ≤ m, 1 ≤ j ≤ n.

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 ...

Barnette's Conjecture: Every 3-connected cubic planar bipartite graph is Hamiltonian. It is known that this is not true if you remove the "bipartite" condition, but the smallest 3-connected cubic ...

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.