39 citations · 203 across the 85 of their papers we have counts for
13 papers · 1 filter
Bounds on graph eigenvalues II
Vladimir Nikiforov
Some recent results on graph eigenvalues are improved. In particular, among all graphs of given order with no cliques of order the -partite Turan graph has maximal spect…
Eigenvalues and forbidden subgraphs I
Vladimir Nikiforov
We present sharp inequalities relating the number of vertices, edges, and triangles of a graph to the smallest eigenvalue of its adjacency matrix and the largest eigenvalue of its…
Linear combinations of graph eigenvalues
Vladimir Nikiforov
Let F(G) be a fixed linear combination of the k extremal eigenvalues of a graph G and of its complement. The problem of finding max{F(G):v(G)=n} generalizes a number of problems ra…
The sum of the squares of degrees: an overdue assignement
Vladimir Nikiforov
Let f(n,m) be the maximum of the sum of the squares of degrees of a graph with n vertices and m edges. Summarizing earlier research, we present a concise, asymptotically sharp uppe…
Graphs and Hermitian matrices: exact interlacing
Bela Bollobas, Vladimir Nikiforov
We prove conditions for equality between the extreme eigenvalues of a matrix and its quotient. In particular, we give a lower bound on the largest singular value of a matrix and ge…
Revisiting two classical results on graph spectra
Vladimir Nikiforov
Let mu(G) and mu_min(G) be the largest and smallest eigenvalues of the adjacency matricx of a graph G. We refine quantitatively the following two results on graph spectra. (i) if H…