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"... Here, for the first time, all connected quartic bi-partite Cayley integral graphs are given includ-ing all non-obvious * isomorphisms. Computations used previous results showing that all connected quartic bipartite integral graphs have one of 43 possible values for the number of vertices, all fallin ..."

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Here, for the first time, all connected quartic bi-partite Cayley integral graphs are given includ-ing all non-obvious * isomorphisms. Computations used previous results showing that all connected quartic bipartite integral graphs have one of 43 possible values for the number of vertices, all falling between 8 and 560. Recently the quartic Cayley integral graphs on finite abelian groups were determined but here we have found the graphs considering all groups. Explaining the Terms An integral graph is a graph with integer eigenvalues with respect to the adjacency ma-trix of the graph. The spectrum of a graph is the eigenvalues with their multiplicity. {4, 06,âˆ’4} The Cayley Graph Cay(G,S) for a given group G and S âŠ‚ G is the graph with vertex set G and with x connected to y if and only if yxâˆ’1 âˆˆ S.