Graphs characterized by the second distance eigenvalue
We characterize all connected graphs with second distance eigenvalue less than $-0.5858$.
math.CO↗
arXiv subjects
Rundan Xing
Publications and source records attributed to Rundan Xing.
Laplacian and signless Laplacian spectral radii of graphs with fixed domination number
In this paper, we determine the maximal Laplacian and signless Laplacian spectral radii for graphs with fixed number of vertices and domination number, and characterize the extremal graphs respectively.
math.CO↗
Bounds for the spectral radius of nonnegative matrices
We give upper and lower bounds for the spectral radius of a nonnegative matrix by using its average 2-row sums, and characterize the equality cases if the matrix is irreducible. We also apply these bounds to various nonnegative matrices associated with a graph, including the adjacency matrix, the signless Laplacian matrix, the distance matrix, the distance signless Laplacian matrix, and the reciprocal distance matrix.
math.CO↗
Ordering trees having small reverse Wiener indices
The reverse Wiener index of a connected graph $G$ is a variation of the well-known Wiener index $W(G)$ defined as the sum of distances between all unordered pairs of vertices of $G$. It is defined as $Λ(G)=\frac{1}{2}n(n-1)d-W(G)$, where $n$ is the number of vertices, and $d$ is the diameter of $G$. We now determine the second and the third smallest reverse Wiener indices of $n$-vertex trees and characterize the trees whose reverse Wiener indices attain these values for $n\ge 6$ (it has been known that the star is the unique tree with the smallest reverse Wiener index).
math.CO↗