Estimation of the maximum multiplicity of an eigenvalue in terms of the vertex degrees of the graph of a matrix.
Extremely Irregular Graphs
Extremum degree sets of irregular oriented graphs and pseudodigraphs
A digraph in which any two vertices have distinct degree pairs is called irregular. Sets of degree pairs for all irregular oriented graphs (also loopless digraphs and pseudodigraphs) with minimum and maximum size are determined. Moreover, a method of constructing corresponding irregular realizations of those sets is given.