论文标题
距离矩阵相关光谱
Distance matrix correlation spectrum of graphs
论文作者
论文摘要
令$ g $为简单的，连接的图，$ \ mathcal {d}（g）$是$ g $的距离矩阵，而$ tr（g）$是$ g $的顶点传输的对角线矩阵。 $ g $的距离拉普拉斯矩阵和无距离的laplacian矩阵由$ \ nathcal {l}（g）= tr（g）= tr（g） - \ Mathcal {d}（g）$ and $ \ nathcal {q}（q} Q}（q}（g）= tr（g）= tr（g）+\ \ \ \ \ mathcal {d d} $，分析。 $ \ MATHCAL {D}（G）$，$ \ MATHCAL {L}（G）$和$ \ MATHCAL {Q}（G）$的特征值称为$ \ Mathcal {d} - $ spectrum，$ spectrum，$ \ mathcal {l} - $ spectrum and $ spectrum and $ \ mathcal and $ \ seppers} - $ g $的广义距离矩阵定义为$ \ nathcal {d}_α（g）=αtr（g）+（1-α）\ Mathcal {d}（g），〜0 \ 0 \leqα\ leq1 $，$ g $ $ g $ $ g）是$ $ $ $ $ $ $ $ $ $ nmate。在本文中，我们对$ \ Mathcal {d} - $ spectrum，$ \ Mathcal {l} - $ spectrum和$ \ Mathcal {q} - $ spectrum的某些图表获得的某些图形频谱。此外，我们基于其他图理论参数的$ g $的广义距离频谱半径及其line Gragr $ l（g）$的广义距离频谱半径，并表征极端图。最后，我们研究了某些复合图的广义距离光谱。
Let $G$ be a simple, connected graph, $\mathcal{D}(G)$ be the distance matrix of $G$, and $Tr(G)$ be the diagonal matrix of vertex transmissions of $G$. The distance Laplacian matrix and distance signless Laplacian matrix of $G$ are defined by $\mathcal{L}(G) = Tr(G)-\mathcal{D}(G)$ and $\mathcal{Q}(G) = Tr(G)+\mathcal{D}(G)$, respectively. The eigenvalues of $\mathcal{D}(G)$, $\mathcal{L}(G)$ and $\mathcal{Q}(G)$ is called the $\mathcal{D}-$spectrum, $\mathcal{L}-$spectrum and $\mathcal{Q}-$spectrum, respectively. The generalized distance matrix of $G$ is defined as $\mathcal{D}_α(G)=αTr(G)+(1-α)\mathcal{D}(G),~0\leqα\leq1$, and the generalized distance spectral radius of $G$ is the largest eigenvalue of $\mathcal{D}_α(G)$. In this paper, we give a complete description of the $\mathcal{D}-$spectrum, $\mathcal{L}-$spectrum and $\mathcal{Q}-$spectrum of some graphs obtained by operations. In addition, we present some new upper and lower bounds on the generalized distance spectral radius of $G$ and of its line graph $L(G)$, based on other graph-theoretic parameters, and characterize the extremal graphs. Finally, we study the generalized distance spectrum of some composite graphs.
