# Search results for: Xueliang Li

Journal of Mathematical Chemistry > 2009 > 45 > 4 > 962-973

*E*of a graph

*G*is equal to the sum of the absolute values of the eigenvalues of

*G*. In 2005 Lin et al. determined the trees with a given maximum vertex degree Δ and maximum

*E*, that happen to be trees with a single vertex of degree Δ. We now offer a simple proof of this result and, in addition, characterize the maximum energy trees having two vertices of maximum degree Δ.

Journal of Mathematical Chemistry > 2007 > 42 > 4 > 775-788

*s*(

*G*) of a graph

*G*is defined as

*s*(

*G*) = max

_{ i,j }|λ

_{ i }− λ

_{ j }|, where the maximum is taken over all pairs of eigenvalues of

*G*. Let

*U*(

*n*,

*k*) denote the set of all unicyclic graphs on

*n*vertices with a maximum matching of cardinality

*k*, and

*U*

^{*}(

*n*,

*k*) the set of triangle-free graphs in

*U*(

*n*,

*k*). In this paper, we determine the graphs with the largest and second largest spectral radius in

*U*

^{*}(

*n*,

*k*),...

Journal of Mathematical Chemistry > 2007 > 42 > 4 > 729-740

*U*(

*k*) be the set of all unicyclic graphs with a perfect matching. Let

*C*

_{ g(G)}be the unique cycle of

*G*with length

*g*(

*G*), and

*M*(

*G*) be a perfect matching of

*G*. Let

*U*

^{0}(

*k*) be the subset of

*U*(

*k*) such that

*g*(

*G*)≡ 0 (mod 4), there are just

*g*/2 independence edges of

*M*(

*G*) in

*C*

_{ g(G)}and there are some...

Journal of Mathematical Chemistry > 2003 > 33 > 3-4 > 189-193

*β*-polynomial

*β*(

*G*,

*C*,

*x*) of a graph

*G*are real. Since then, there has been some literature intending to solve this conjecture. However, in all existing literature, only classes of graphs were found to show that the conjecture is true; for example, monocyclic graphs, bicyclic graphs, graphs such that no two circuits share a common edge, graphs...