15 citations · 30 across the 15 of their papers we have counts for
16 papers
Eigenvalue problems of Nordhaus-Gaddum type
Vladimir Nikiforov
In 1970 Nosal gave upper and lower bounds on the sum of the spectral radii of a graph and its complement. We generalize this problem to other eigenvalues and give a number of bound…
Eigenvalues and degree deviation in graphs
Vladimir Nikiforov
Given a graph G of order n and size m, let s(G)= sum|d(u)-2m/n|, where the sum is taken over all vertices u of G. We investigate upper and lower bounds on eigenvalues of G in terms…
Walks and the spectral radius of graphs
Vladimir Nikiforov
We give upper and lower bounds on the spectral radius of a graph in terms of the number of walks. We generalize a number of known results.
The minimum number of 4-cliques in graphs with triangle-free complement
Vladimir Nikiforov
Write f(n) for the minimum number of 4-cliques in graphs of order n with triangle-free complement. Finding f(n) is a particular case of a problem raised by Erdos in 1962. We give a…
The sum of degrees in cliques
B. Bollobas, V. Nikiforov
We investigate lower bounds on the average degree in r-cliques in graphs of order n and size greater than t(r,n), where t(r,n) is the size of the Turan graph on n vertices and r co…
Joints in graphs
B. Bollobas, V. Nikiforov
In 1969 Erdoes found a lower bound on the number of (r+1)-cliques sharing an edge in graphs with n vertices and t(r,n)+1 edges, where t(r,n) is the size of the Turan graph of order…