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| s2cid = 32070167
| url = https://research.tilburguniversity.edu/en/publications/a9a1857e-13ce-4da7-bcca-b879f9f3215f
| doi-access = free
}}. See in particular Proposition 8, p. 262.</ref> They may also be characterized (again with the exception of {{math|''K''{{sub|8}}}}) as the [[strongly regular graph]]s with parameters {{math|srg(''n''(''n'' – 1)/2, 2(''n'' – 2), ''n'' – 2, 4)}}.<ref>{{harvtxt|Harary|1972}}, Theorem 8.6, p. 79. Harary credits this result to independent papers by L. C. Chang (1959) and [[Alan Hoffman (mathematician)|A. J. Hoffman]] (1960).</ref> The three strongly regular graphs with the same parameters and spectrum as {{math|''L''(''K''{{sub|8}})}} are the [[Chang graphs]], which may be obtained by [[Two-graph|graph switching]] from {{math|''L''(''K''{{sub|8}})}}.
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| volume = 309
| year = 2009| s2cid = 16049392
| doi-access = free
}}.</ref> A special case of these graphs are the [[rook's graph]]s, line graphs of [[complete bipartite graph]]s. Like the line graphs of complete graphs, they can be characterized with one exception by their numbers of vertices, numbers of edges, and number of shared neighbors for adjacent and non-adjacent points. The one exceptional case is {{math|''L''(''K''{{sub|4,4}})}}, which shares its parameters with the [[Shrikhande graph]]. When both sides of the bipartition have the same number of vertices, these graphs are again strongly regular.<ref>{{harvtxt|Harary|1972}}, Theorem 8.7, p. 79. Harary credits this characterization of line graphs of complete bipartite graphs to Moon and Hoffman. The case of equal numbers of vertices on both sides had previously been proven by Shrikhande.</ref>
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