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Note on the minimal size of a graph with generalized connectivity kappa_3= 2
Shasha Li, Xueliang Li, Yongtang Shi
The concept of generalized -connectivity of a graph was introduced by Chartrand et al. in recent years. In our early paper, extremal theory for this graph paramet…
On the maximal energy tree with two maximum degree vertices
Jing Li, Xueliang Li, Yongtang Shi
For a simple graph , the energy is defined as the sum of the absolute values of all eigenvalues of its adjacent matrix. For and , denote by …
Solution to a conjecture on the maximal energy of bipartite bicyclic graphs
Bofeng Huo, Shengjin Ji, Xueliang Li +1
The energy of a simple graph , denoted by , is defined as the sum of the absolute values of all eigenvalues of its adjacency matrix. Let denote the cycle of order $n…
Rainbow connections of graphs -- A survey
Xueliang Li, Yuefang Sun
The concept of rainbow connection was introduced by Chartrand et al. in 2008. It is fairly interesting and recently quite a lot papers have been published about it. In this survey…
The complexity of determining the rainbow vertex-connection of graphs
Lily Chen, Xueliang Li, Yongtang Shi
A vertex-colored graph is {\it rainbow vertex-connected} if any two vertices are connected by a path whose internal vertices have distinct colors, which was introduced by Krivelevi…
Note on a relation between Randic index and algebraic connectivity
Xueliang Li, Yongtang Shi
A conjecture of AutoGraphiX on the relation between the Randić index and the algebraic connectivity of a connected graph is: $$\frac R a\leq (\frac{n-3+2\sqrt{2}}{2})/(…