论文标题
合并套件的补充
Complements of coalescing sets
论文作者
论文摘要
我们认为表格$ QD+a $的矩阵，其中$ d $是对角度矩阵，$ a $作为邻接矩阵，而$ q $是固定值。给定我们称之为融合的$（h，b）$的图形$ h $和$ h $和$ b \ subseteq v（g）$，我们得出了特征多项式的公式，其中root附加了同一rooted Graph $ g $的副本，将根连接到\ emph {everph {avery} vertertex of $ b $。此外，我们确定$（h_1，b_1）$和$（h_2，b_2）$是两个合并对的，对于任何可能的根graph $ g $，然后是$（h_1），v（h_1）\ setminus b_1）$和$（H_2，v（h_2），v（h_2）\ setminus b_2 $ yous at peccect as cosminus $ geccect as as as as cost $ geccect as as as as as as costral，$（h_1）\ setminus b_1）$（h_1）\ setminus b_1）是$ GEAR的。
We consider matrices of the form $qD+A$, with $D$ being the diagonal matrix of degrees, $A$ being the adjacency matrix, and $q$ a fixed value. Given a graph $H$ and $B\subseteq V(G)$, which we call a coalescent pair $(H,B)$, we derive a formula for the characteristic polynomial where a copy of same rooted graph $G$ is attached by the root to \emph{each} vertex of $B$. Moreover, we establish if $(H_1,B_1)$ and $(H_2,B_2)$ are two coalescent pairs which are cospectral for any possible rooted graph $G$, then $(H_1,V(H_1)\setminus B_1)$ and $(H_2,V(H_2)\setminus B_2)$ will also always be cospectral for any possible rooted graph $G$.
