53 citations · 63 across the 16 of their papers we have counts for
6 papers · 1 filter
Laplacian eigenvalue distribution, diameter and domination number of trees
Jiaxin Guo, Jie Xue, Ruifang Liu
For a graph with domination number , Hedetniemi, Jacobs and Trevisan [European Journal of Combinatorics 53 (2016) 66-71] proved that , where m…
A Framework for Approximation Schemes on Disk Graphs
Daniel Lokshtanov, Fahad Panolan, Saket Saurabh +2
We initiate a systematic study of approximation schemes for fundamental optimization problems on disk graphs, a common generalization of both planar graphs and unit-disk graphs. Ou…
Maxima of spectral radius of irregular graphs with given maximum degree
Jie Xue, Ruifang Liu
Let be the maximum spectral radius of connected irregular graphs on vertices with maximum degree . Liu, Shen and Wang (2007) conjectured that $\lim_{n\rightarrow \in…
Maxima of the -index of non-bipartite -free graphs
Ruifang Liu, Lu Miao, Jie Xue
A classic result in extremal graph theory, known as Mantel's theorem, states that every non-bipartite graph of order with size contains a tri…
Cubic bipartite graphs with minimum spectral gap
Ruifang Liu, Jie Xue
The difference between the two largest eigenvalues of the adjacency matrix of a graph is called the spectral gap of If is a regular graph, then its spectral gap is equ…
The maximum spectral radius of irregular bipartite graphs
Jie Xue, Ruifang Liu, Jiaxin Guo +1
A bipartite graph is subcubic if it is an irregular bipartite graph with maximum degree three. In this paper, we prove that the asymptotic value of maximum spectral radius over sub…