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Following suggestions for my post here "Should results of a journal paper always be reproducible?", I have done the simulation using a particular seed in the first part of my result section. Now the issues are, how to mention that particular seed in the paper. I have not come across any particular paper doing so. For this reason, I am uncertain about mentioning it.

Any reference of how people do this would be highly appreciable.

Meanwhile, following is what I am writing

In practice, nodes can be distributed in a large number of topologies. However, the results in Fig. 2,3, and 4 follow a fixed topology generated by pseudo-random seed (1010) to validate the scheme. Later, a more comprehensive analysis is shown in Fig. 5 and Table I.

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    A side point (covered in the linked question but which bears repeating): if your conclusions depend on the particular seed being used, you're likely doing something wrong. That is to say, people should be able to replicate your conclusions with any arbitrary seed - or indeed, any arbitrary (decent) random number generator. The particular numbers/examples might change, but the overall conclusion should be robust. Providing a particular seed is more "belt and braces", so that people can troubleshoot why they can't replicate with a different seed/generator.
    – R.M.
    Commented Jun 6, 2018 at 14:36

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A seed for a pseudo-random number generator is a sufficiently well-known concept in numerical simulations that the seed, on its own, probably does not require a citation—you can simply state which seed you used. The pseudo-random number generator algorithm, however, may need to be cited, particularly if it's not a well-known algorithm.

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If you are aiming for your results to be completely reproducible, you will need the random-generator seed, however you will also need the source code (unless you use only one predefined method in a very clear way) and sometimes even other information such as the version of employed software, operating system, and hardware specs. The random seed is of no use to the reader on its own, and hence there is no point in mentioning it here.

In most contexts, I would only state in the main text which realisations are identical. That you control this with seeds (instead of say saving and loading them) is a technical detail that should have no relevance to your results. I would put the seeds together with the source code and other relevant details in a supplement (or similar). At most I would mention the specific seed when referencing this supplement in a way that makes clear to the reader that this information only makes sense together with the supplement:

The results in Fig. 2, 3, and 4 were obtained for the same realisation of the topology (Supplement A, seed 1010) to validate the scheme.

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    Not even the same software version is necessarily sufficient to reproduce; the OS and even the hardware architecture would also need to be described.
    – user9482
    Commented Jun 5, 2018 at 14:48

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