Maxima of the Q-index: Forbidden even cycles

Nikiforov, Vladimir; Yuan, Xiying

doi:10.1016/j.laa.2015.01.019

Cited by 22 publications

(10 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Clearly, we can see that S + n,k does not contain C 2k+2 as a subgraph. It was proved by Nikiforov and Yuan [148] that ex q (n,…”

Section: Spectral Problem For General Graphsmentioning

confidence: 99%

A survey on spectral conditions for some extremal graph problems

Li,

Liu,

Feng

2021

Preprint

View full text Add to dashboard Cite

This survey is two-fold. We first report new progress on the spectral extremal results on the Turán type problems in graph theory. More precisely, we shall summarize the spectral Turán function in terms of the adjacency spectral radius and the signless Laplacian spectral radius for various graphs. For instance, the complete graphs, general graphs with chromatic number at least three, complete bipartite graphs, odd cycles, even cycles, color-critical graphs and intersecting triangles.The second goal is to conclude some recent results of the spectral conditions on some graphical properties. By a unified method, we present some sufficient conditions based on the adjacency spectral radius and the signless Laplacian spectral radius for a graph to be Hamiltonian, k-Hamiltonian, k-edge-Hamiltonian, traceable, k-pathcoverable, k-connected, k-edge-connected, Hamilton-connected, perfect matching and β-deficient.

show abstract

“…Clearly, we can see that S + n,k does not contain C 2k+2 as a subgraph. It was proved by Nikiforov and Yuan [148] that ex q (n,…”

Section: Spectral Problem For General Graphsmentioning

confidence: 99%

A survey on spectral conditions for some extremal graph problems

Li,

Liu,

Feng

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Many instances of Problem B have been solved, see, e.g., the second part of the survey paper [25]. There is also considerable progress with Problem C: see, e.g., the papers [1], [2], [14], [15], [17], [26], [27], [28], and [30]. Now, having the family A α (G), we can merge Problems B and C into one, namely:…”

Section: Problem a Given A Graph F What Is The Maximum Number Of Edge...mentioning

confidence: 99%

Merging the A-and Q-spectral theories

Nikiforov

2017

Appl Anal Discrete Math

245

148

View full text Add to dashboard Cite

Let G be a graph with adjacency matrix A (G), and let D (G) be the diagonal matrix of the degrees of G. The signless LaplacianCvetković called the study of the adjacency matrix the A-spectral theory, and the study of the signless Laplacian-the Q-spectral theory. During the years many similarities and differences between these two theories have been established. To track the gradual change of A (G) into Q (G) in this paper it is suggested to study the convex linear combinations A α (G) of A (G) and D (G) defined byThis study sheds new light on A (G) and Q (G), and yields some surprises, in particular, a novel spectral Turán theorem. A number of challenging open problems are discussed.

show abstract

“…In [6], Nikiforov and Yuan studied how large can q 1 (G) be if G is a graph of order n and contains no cycle of given even length and presented the following result:…”

Section: Even/odd Cycle-free Graphsmentioning

confidence: 99%