Extremal graph on normalized Laplacian spectral radius and energy

  title={Extremal graph on normalized Laplacian spectral radius and energy},
  author={Kinkar Chandra Das and Shaowei Sun},
  journal={Electronic Journal of Linear Algebra},
  • K. Das, Shaowei Sun
  • Published 22 December 2016
  • Mathematics
  • Electronic Journal of Linear Algebra
Let G = (V, E) be a simple graph of order n and the normalized Laplacian eigenvalues ρ1 ≥ ρ2 ≥ · · · ≥ ρn−1 ≥ ρn = 0. The normalized Laplacian energy (or Randić energy) of G without any isolated vertex is defined as 
Normalized Laplacian eigenvalues with chromatic number and independence number of graphs
ABSTRACT Let be the normalized Laplacian eigenvalues of a graph G with n vertices. Also, let χ and α be the chromatic number and the independence number of a graph G, respectively. In this paper, we
Spectral Gap of the Largest Eigenvalue of the Normalized Graph Laplacian
We offer a new method for proving that the maximal eigenvalue of the normalized graph Laplacian of a graph with $n$ vertices is at least $\frac{n+1}{n-1}$ provided the graph is not complete and that
Petals and Books: The largest Laplacian spectral gap from 1
We prove that, for any connected graph on N ≥ 3 vertices, the spectral gap from the value 1 with respect to the normalized Laplacian is at most 1 / 2. Moreover, we show that equality is achieved if
On the normalized Laplacian spectral radii of a graph and its line graph
The extremal graph for the minimum normalized Laplacian spectral radii of nearly complete graphs is determined and several lower bounds are presented in terms of graph parameters and characterize the extremal graphs.


Bounds on normalized Laplacian eigenvalues of graphs
Let G be a simple connected graph of order n, where n≥2. Its normalized Laplacian eigenvalues are 0=λ1≤λ2≤⋯≤λn≤2. In this paper, some new upper and lower bounds on λn are obtained, respectively.
On the normalized Laplacian eigenvalues of graphs
This is a book about the normalized Laplacian eigenvalues of a graph, which contains the research results during my Ph.D study in Sungkyunkwan University, Suwon, Korea. The normalized Laplacian
On Randic Energy of Graphs
Let G =( V, E )b e as i mple graph with vertex set V (G )= {v1 ,v 2 ,..., vn} and edge set E(G). The Randic matrix R =( rij) of a graph G whose vertex vi has degree di is defined by rij =1 / � didj
On the normalized Laplacian energy and general Randić index R-1 of graphs
On Randić energy
On graphs with at least three distance eigenvalues less than −1☆
To any graph we may associate a matrix which records information about its structure. The goal of spectral graph theory is to see how the eigenvalues of such a matrix representation relate to the
Trees with 4 or 5 distinct normalized Laplacian eigenvalues