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I need to solve how to construct regular graphs with girth at least five, if girth is five, I know Petersen Graph and a circle satisfy the condition. But is there any other regular graphs with girth five (In fact I want $k$-regular graphs)? What if the girth is more than five?

Sincerely thanks your help.

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    Well, a cyclic graph on $n$ vertices is 2-regular of girth $n$ – 2017-01-24
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    @HagenvonEitzen Thanks, I noticed it just now, but I want $k-$regular graphs. – 2017-01-24
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    The graph of a dodecahedron is $3$-regular of girth $5.$ – 2017-01-24
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    The point-line incidence graph of a projective plane of order $n$ is an $(n+1)$-regular graph of girth $6.$ – 2017-01-24
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    Xavier Dahan, Regular graphs of large girth and arbitrary degree, is available at https://arxiv.org/abs/1110.5259 – see also http://www.math.uchicago.edu/~may/VIGRE/VIGRE2007/REUPapers/FINALAPP/Ullery.pdf – 2017-01-24
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    Any thoughts, Lorence, on the comments? Have you had a look at the links? – 2017-01-25
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    Are you still here, Lorence? – 2017-01-27
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    @GerryMyerson So sorry, I did not check the stackexchange those days. I just downloaded the pdf, thank you very much, I will read it carefully, sorry again. – 2017-01-28

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