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How can we show that the intersection graph of the Desargues configuration, the line graph of $K_5$ and the complement of the Petersen graph is isomorphic to each other.

My try:I know their individual properties but the problem is that how I approach to show isomorphic.

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    If you have concrete descriptions/drawings of each of the graphs, it's just a matter of writing down an actual isomorphism, possibly in table form. – 2017-02-27
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    As I infer from the line graph case, your graphs may have "only" 10 vertices, so you can check this by hand, as Henning said. – 2017-02-27

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