论文标题
在线图的双盖上
On the double covers of a line graph
论文作者
论文摘要
令$ l（x）$为图$ x $的线图。令$ x^{\ prime \ prime} $为$ k_2 $的$ x $的Kronecker产品。在本文中，我们看到$ l（x^{\ prime \ prime}）$是$ l（x）$的双重封面。我们定义了$ x $的对称边缘图，称为$γ（x）$，也是$ l（x）$的双重封面。我们研究了$γ（x）$的各种属性，以及$ x $的关系，以及$ l（x）$的三个双重封面之间的关系，即$ l（x^{\ prime \ prime}），γ（x）$和$ l（x）^{\ prime \ prime \ prime} $。在这些双重封面的帮助下，我们表明，对于任何整数$ k \ geq 5 $，都有两个不可察觉的订单$ 2K $的均等图。
Let $L(X)$ be the line graph of graph $X$. Let $X^{\prime\prime}$ be the Kronecker product of $X$ by $K_2$. In this paper, we see that $L(X^{\prime\prime})$ is a double cover of $L(X)$. We define the symmetric edge graph of $X$, denoted as $γ(X)$ which is also a double cover of $L(X)$. We study various properties of $γ(X)$ in relation to $X$ and the relationship amongst the three double covers of $L(X)$ that are $L(X^{\prime\prime}),γ(X)$ and $L(X)^{\prime\prime}$. With the help of these double covers, we show that for any integer $k\geq 5$, there exist two equienergetic graphs of order $2k$ that are not cospectral.
