A graph G is said to be planar if G can be drawn on the plane in such a way that its edges intersect only at their endpoints.In this paper,all the planar graphs without isolated vertices whose second largest eigenvalu...A graph G is said to be planar if G can be drawn on the plane in such a way that its edges intersect only at their endpoints.In this paper,all the planar graphs without isolated vertices whose second largest eigenvalue smaller than(√5-1)/2 are characterized.展开更多
A connected graph G=(V,E)is called a quasi-tree graph if there exists a vertex v0∈V(G)such that G-v0 is a tree.In this paper,we determine all quasi-tree graphs of order n with the second largest signless Laplacian ei...A connected graph G=(V,E)is called a quasi-tree graph if there exists a vertex v0∈V(G)such that G-v0 is a tree.In this paper,we determine all quasi-tree graphs of order n with the second largest signless Laplacian eigenvalue greater than or equal to n-3.As an application,we determine all quasi-tree graphs of order n with the sum of the two largest signless Laplacian eigenvalues greater than to 2 n-5/4.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.12171154)。
文摘A graph G is said to be planar if G can be drawn on the plane in such a way that its edges intersect only at their endpoints.In this paper,all the planar graphs without isolated vertices whose second largest eigenvalue smaller than(√5-1)/2 are characterized.
基金Supported by the National Natural Science Foundation of China(Grant No.11771443)the Fundamental Research Funds for the Central Universities(Grant No.2018BSCXB24)the Postgraduate Research&Practice Innovation Program of Jiangsu Province(Grant No.KYCX18JL980).
文摘A connected graph G=(V,E)is called a quasi-tree graph if there exists a vertex v0∈V(G)such that G-v0 is a tree.In this paper,we determine all quasi-tree graphs of order n with the second largest signless Laplacian eigenvalue greater than or equal to n-3.As an application,we determine all quasi-tree graphs of order n with the sum of the two largest signless Laplacian eigenvalues greater than to 2 n-5/4.
