作业帮求高手帮忙翻译下英文文献
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求高手帮忙翻译下英文文献
in this paper,we consider only simple connected graphs and follow the notation
of [1].Let G be a simple graph with vertex set V(G) and edge set E(G). The
adjacency matrix of G is A(G) = (J), where J = 1 if two vertices iand j are
adjacent in G and J = 0 otherwise. The characteristic polynomial of G is just
PG(x) = det(xI− A(G)). Let D(G) be the diagonal degree matrix of G. We
call the matrix Q(G) = D(G) − A(G) the Laplacian matrix of G, and the matrix
Q(G) = D(G) + A(G) the signless Laplacian matrix or Q-matrix of G. We denote
the largest eigenvalues of A(G), L(G),Q(G) by P(G), J(G), U(G), respectively, and
call them the adjacency spectral radius, the Laplacian spectral radius, the signless
Laplacian spectral radius (or the Q-spectral radius) of G, respectively.
The study of the signless Laplacian spectral radius has recently attracted re-
searchers’ attention. In [10], Fan et al. studied the signless Laplacian spectral
radius of bicyclic graphs with fixed order. In [9], the authors discussed the smallest
eigenvalue of Q(G) as a parameter reflecting the nonbipartiteness of the graph G.
In [7], the authors studied the smallest signless Laplacian eigenvalue of non-bipartite
graphs. In [11], the extremal graphs with maximal signless Laplacian spectral ra-
dius and fixed diameter were studied. More information about the signless Lapla-
cian can be found in [2], [3], [5], [6]. For more information about the spectral
radius of graphs, the reader can refer to [4].
in this paper,we consider only simple connected graphs and follow the notation
of [1].Let G be a simple graph with vertex set V(G) and edge set E(G). The
adjacency matrix of G is A(G) = (J), where J = 1 if two vertices iand j are
adjacent in G and J = 0 otherwise. The characteristic polynomial of G is just
PG(x) = det(xI− A(G)). Let D(G) be the diagonal degree matrix of G. We
call the matrix Q(G) = D(G) − A(G) the Laplacian matrix of G, and the matrix
Q(G) = D(G) + A(G) the signless Laplacian matrix or Q-matrix of G. We denote
the largest eigenvalues of A(G), L(G),Q(G) by P(G), J(G), U(G), respectively, and
call them the adjacency spectral radius, the Laplacian spectral radius, the signless
Laplacian spectral radius (or the Q-spectral radius) of G, respectively.
The study of the signless Laplacian spectral radius has recently attracted re-
searchers’ attention. In [10], Fan et al. studied the signless Laplacian spectral
radius of bicyclic graphs with fixed order. In [9], the authors discussed the smallest
eigenvalue of Q(G) as a parameter reflecting the nonbipartiteness of the graph G.
In [7], the authors studied the smallest signless Laplacian eigenvalue of non-bipartite
graphs. In [11], the extremal graphs with maximal signless Laplacian spectral ra-
dius and fixed diameter were studied. More information about the signless Lapla-
cian can be found in [2], [3], [5], [6]. For more information about the spectral
radius of graphs, the reader can refer to [4].
在本文中,我们只考虑简单连通图,并按照符号
[1].设G是一个集V（G）和边集简单图顶点为E（G）.该
G的邻接矩阵是一个（g）=（j）项,其中J=1如果两个顶点i和j是
在G和J毗邻=否则为0.G的特征多项式就是
编程器（十）= DET的（西一个（g））.设D（G）是G的对角矩阵的程度,我们
调用矩阵Q（G）的= D类（G）的-阿（G）为G的拉普拉斯矩阵,矩阵
问（七）= D类（G）的+一（G）的无符号Laplacian矩阵或Q- G的矩阵,记
最大特征值的一个（g）,升（七）,问（七）由P（七）,J类（G）的铀（G）的,分别与
称他们为邻接谱半径,拉普拉斯谱半径,无符号
Laplace谱半径（或的Q谱半径）G的分别.
该无符号Laplace谱半径研究最近吸引了重
搜索用户的注意力.[10],范等.研究了无符号Laplace谱
半径与固定阶双圈图.[9]中,作者讨论了最小
特征值的Q（七）作为参数反映了克图nonbipartiteness
[7]中,作者研究了最小的无符号的非二部的Laplacian特征值
图表.[11],用极图的最大无符号Laplace谱镭
半径和固定的直径进行了研究.更多有关无符号Lapla-
奇安中可以找到[2][3],[5] [6].如需有关的光谱资料
图的半径,
[1].设G是一个集V（G）和边集简单图顶点为E（G）.该
G的邻接矩阵是一个（g）=（j）项,其中J=1如果两个顶点i和j是
在G和J毗邻=否则为0.G的特征多项式就是
编程器（十）= DET的（西一个（g））.设D（G）是G的对角矩阵的程度,我们
调用矩阵Q（G）的= D类（G）的-阿（G）为G的拉普拉斯矩阵,矩阵
问（七）= D类（G）的+一（G）的无符号Laplacian矩阵或Q- G的矩阵,记
最大特征值的一个（g）,升（七）,问（七）由P（七）,J类（G）的铀（G）的,分别与
称他们为邻接谱半径,拉普拉斯谱半径,无符号
Laplace谱半径（或的Q谱半径）G的分别.
该无符号Laplace谱半径研究最近吸引了重
搜索用户的注意力.[10],范等.研究了无符号Laplace谱
半径与固定阶双圈图.[9]中,作者讨论了最小
特征值的Q（七）作为参数反映了克图nonbipartiteness
[7]中,作者研究了最小的无符号的非二部的Laplacian特征值
图表.[11],用极图的最大无符号Laplace谱镭
半径和固定的直径进行了研究.更多有关无符号Lapla-
奇安中可以找到[2][3],[5] [6].如需有关的光谱资料
图的半径,