Most strongly regular graphs have trivial first clique homology; non-vanishing occurs only for listed families including Petersen, lattice graphs, and certain conference graphs, with explicit homology dimensions computed for Latin square graphs.
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On the homology groups of clique complexes of strongly regular graphs
Most strongly regular graphs have trivial first clique homology; non-vanishing occurs only for listed families including Petersen, lattice graphs, and certain conference graphs, with explicit homology dimensions computed for Latin square graphs.