Nullity of Graphs: An Updated Survey
Ivan Gutman, Bojana Borovićanin (2011)
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Nullity of Graphs: An Updated Survey
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Suppose that G is a simple, vertex-labeled graph and that S is a multiset. Then if there exists a one-to-one mapping between the elements of S and the vertices of G, such that edges in G exist if and only if the absolute difference of the corresponding vertex labels exist in S, then G is an autograph, and S is a signature for G. While it is known that many common families of graphs are autographs, and that infinitely many graphs are not autographs, a non-autograph has never been exhibited....
DISTANCE SPECTRA AND DISTANCE ENERGIES OF ITERATED LINE GRAPHS OF REGULAR GRAPHS
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