On the Distance Spectra of Extended Double Stars

Extended double covers of non-symmetric association schemes of class $2$

In this paper, we give a method to construct non-symmetric association schemes of class $3$ from non-symmetric association schemes of class $2$. This construction is a non-symmetric analogue of the construction of Taylor graphs as an antipodal double cover of a complete graph. We also mention how our construction interact with doubling introduced by Pasechnik.

Distance spectra of some double join of graphs and some new families of distance equienergetic graphs

In this paper we compute the spectrum of a special block matrix and use it to describe the distance spectra of some double join of graphs. As an application, we give several families of distance equienergetic graphs of diameter 3.

On the Laplacian spectra of some double join operations of graphs

Many variants of join operations of graphs have been introduced and their spectral properties have been studied extensively by many researchers. This paper mainly focuses on the Laplacian spectra of some double join operations of graphs. We first introduce the conception of double join matrix and provide a complete information about its eigenvalues and the corresponding eigenvectors. Further, we define four variants of double join operations based on subdivision graph, $Q$-graph, $R$-graph and total graph. Applying the result obtained for the double join matrix, we give an explicit complete ch…

闭邻域超图的射影维数：通过扩展二重覆盖

Projective dimension of closed neighborhood hypergraphs via extended double covers

本文研究无孤立顶点图的闭邻域超图射影维数与扩展二部二重覆盖的正则性关系，证明一般上界，并在多类图上建立精确等式，方法结合覆盖、支配、匹配参数与同调工具。

倍图的能量、Laplacian能量和新的等能图族

Energy, Laplacian energy of double graphs and new families of equienergetic graphs

对于一个顶点集为$V(G)=\{v_1, v_2, \cdots, v_n\}$的图$G$，扩展的双覆盖$G^*$是一个具有二分图（X，Y），$X=\{x_1, x_2, \cdots, x_n\}$和$Y=\{y_1, y_2, \cdots, y_n\}$的二分图，其中两个顶点$x_i$和$y_j$相邻当且仅当$G$中的$i=j$或$v_i$与$v_j$相邻. $G$的双图$D[G]$是通过取$G$的两个副本并将一个副本中的每个顶点与另一个副本中相应顶点的邻居连接而获得的图。本文研究了$G$的$k$ -次迭代扩张双覆盖的$G^{k*}$的$G^*$和$D[G]$，$L$ -谱的能量和Laplacian能量.得到了$G^*$的生成树个数的计算公式。我们还得到了一些新的等能图族和$L$ -等能图族.

The normalized Laplacian spectra of the double corona based on $R$-graph

For simple graphs $G$, $G_1$ and $G_2$, we denote their double corona based on $R$-graph by $G^{(R)}\otimes{\{G_1,G_2\}}$. This paper determines the normalized Laplacian spectrum of $G^{(R)}\otimes{\{G_1,G_2\}}$ in terms of these of $G$, $G_1$ and $G_2$ whenever $G$, $G_1$ and $G_2$ are regular. The obtained result reduces to the normalized Laplacian spectra of the $R$-vertex corona $G^{(R)}\odot{G_1}$ and $R$-edge corona $G^{(R)}\circleddash{G_2}$ by choosing $G_2$ or $G_1$ as a null-graph, respectively. Finally, applying the results of the paper, we construct infinitely many pairs of normali…