Talk:Integral graph
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Integral graph
The line graph of a non-regular integral graph is not necessarily integral. Consider $K2\lor3K_1$ (a single edge $ab$ plus $3$ vertices that are adjacent to both $a$ and $b$). It has spectrum [3, 0, 0, -1, -2], but its line graph has spectrum [4.372281323269015?, 1, 0, 0, -1.372281323269015?, -2, -2]. I added the word "regular" to the page. Leen Droogendijk (talk) 10:30, 10 April 2025 (UTC)