On graphs with 2 trivial distance ideals
classification
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math.AC
keywords
distancegraphsidealsfamilytrivialgraphmatrixclasses
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Distance ideals generalize the Smith normal form of the distance matrix of a graph. The family of graphs with 2 trivial distance ideals contains the family of graphs whose distance matrix has at most 2 invariant factors equal to 1. Here we give an infinite family of forbidden induced subgraphs for the graphs with 2 trivial distance ideals. These are also related with other well known graph classes.
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