A strong edge coloring of a graph G is a proper edge coloring such that every color class is an induced matching. In 2018, Yang and Wu proposed a conjecture that every generalized Petersen graph $P(n,k)$ with $k\ge 4$ and $n>2k$ can be strong edge colored with (at most) seven colors. Although the generalized Petersen graph $P(n,k)$ is a kind of special graph, the strong chromatic index of $P(n,k)$ is still unknown. In this paper, we support the conjecture by showing that the strong chromatic index of every generalized Petersen graph $P(n,k)$ with $k\ge 4$ and $n>2k$ is at most 9.

中文翻译：

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广义Petersen图的强边着色

图G的强边缘着色是适当的边缘着色，以使每个颜色类别都是诱导匹配。杨和吴在2018年提出了一个猜想，即每个广义Petersen图$P（ñ，ķ）$ 与 $ķ\ge 4$ 和 $ñ>2ķ$可以是最多（最多）七种颜色的坚硬边缘。虽然广义的Petersen图$P（ñ，ķ）$ 是一种特殊的图形， $P（ñ，ķ）$仍然未知。在本文中，我们通过证明每个广义Petersen图的强色指数来支持该猜想$P（ñ，ķ）$ 与 $ķ\ge 4$ 和 $ñ>2ķ$ 最多为9。