论文标题
关于循环，路径和某些树木之间光谱距离的猜想
A conjecture about spectral distances between cycles, paths and certain trees
论文作者
论文摘要
我们确认[{\ em lineal代数及其应用}中提出的以下猜想，{\ bf 436}（2012），第5、1425-1435号。]：$ $ 0.945 \ lim_ \ infty}σ（p_n，z_n）= \ displayStyle \ lim_ {n \ longrightArrow \ infty}σ（w_n，z_n）= \ frac {1} {2} {2} {2} \ lim_ \ displaystyle \ lim_ {n \ longrightArrow \ infty}σ（c_ {2n}，z__ {2n}）= 2，$σ（g_1，g_2，g_2）= \ sum_ = \ sum_ {i = 1}图形$ g_1 $和$ g_2 $带有邻接光谱$λ_1（g_i）\geqλ_2（g_i）\ geq \ geq \ cdots \geqλ_n（g_i）$ for $ i = 1,2 $，$ i = 1,2 $，以及$ p_n $和$ p_n $和$ c_n $表示$ n $ n $ n $ vertices，分别为$ n $ vertices; $ z_n $表示$ p_ {n-2} $的合并和$ p_3 $在$ p_ {n-2} $的1个顶点和$ 2 $ $ p_3 $的顶点;和$ w_n $表示$ z_ {n-2} $的合并，$ z_ {n-2} $的1级顶点的$ p_3 $，该$ z_ {n-2} $毗邻$ 2 $的顶点，$ 2 $的顶点和$ 2 $ $ p_3 $的$ 2 $。
We confirm the following conjecture which has been proposed in [{\em Linear Algebra and its Applications}, {\bf 436} (2012), No. 5, 1425-1435.]: $$ 0.945\approx\displaystyle\lim_{n\longrightarrow \infty}σ(P_n,Z_n)=\displaystyle\lim_{n\longrightarrow \infty}σ(W_n,Z_n)=\frac{1}{2}\displaystyle\lim_{n\longrightarrow \infty}σ(P_n,W_n);\ \displaystyle\lim_{n\longrightarrow \infty}σ(C_{2n},Z_{2n})=2,$$ where $σ(G_1,G_2)=\sum_{i=1}^n |λ_i(G_1)-λ_i(G_2)|$ is the spectral distance between $n$ vertex non-isomorphic graphs $G_1$ and $G_2$ with adjacency spectra $λ_1(G_i) \geq λ_2(G_i) \geq \cdots \geq λ_n(G_i)$ for $i=1,2$, and $P_n$ and $C_n$ denote the path and cycle on $n$ vertices, respectively; $Z_n$ denotes the coalescence of $P_{n-2}$ and $P_3$ on one of the vertices of degree 1 of $P_{n-2}$ and the vertex of degree $2$ of $P_3$; and $W_n$ denotes the coalescence of $Z_{n-2}$ and $P_3$ on the vertex of degree 1 of $Z_{n-2}$ which is adjacent to a vertex of degree $2$ and the vertex of degree $2$ of $P_3$.
