Some star complements for the second largest eigenvalue of a graph

Some Inequalities For The Largest Eigenvalue Of A Graph

Combinatorics, Probability & Computing / Volume 11 / Issue 02 / March 2002, pp 179 189 DOI: 10.1017/S0963548301004928, Published online: 25 April 2002 Link to this article: http://journals.cambridge.org/abstract_S0963548301004928 How to cite this article: V. NIKIFOROV (2002). Some Inequalities for the Largest Eigenvalue of a Graph. Combinatorics, Probability & Computing, 11, pp 179-189 doi:10.1...

On the second largest eigenvalue of a mixed graph

Let G be a mixed graph. We discuss the relation between the second largest eigenvalue λ2(G) and the second largest degree d2(G), and present a sufficient condition for λ2(G) ≥ d2(G).

The second largest eigenvalue of trees

Graphs with prescribed star complement for 1 as the second largest eigenvalue

Let G be a graph of order n and let μ be an eigenvalue of multiplicity m. A star complement for μ in G is an induced subgraph of G of order n −m with no eigenvalue μ. In this paper, we study maximal and regular graphs which have Kr,s + tK1 as a star complement for 1 as the second largest eigenvalue. It turns out that some well known strongly regular graphs are uniquely determined by such a star...

Graphs with small second largest Laplacian eigenvalue

Let L(G) be the Laplacian matrix of G. In this paper, we characterize all of the connected graphs with second largest Laplacian eigenvalue no more than l; where l . = 3.2470 is the largest root of the equation μ3 − 5μ2 + 6μ − 1 = 0. Moreover, this result is used to characterize all connected graphs with second largest Laplacian eigenvalue no more than three. © 2013 Elsevier Ltd. All rights rese...