Journal article
Edge reconstruction of the Ihara zeta function
We show that if a graph G has average degree (d)over-bar >= 4, then the Ihara zeta function of G is edge-reconstructible. We prove some general spectral properties of the edge adjacency operator T: it is symmetric for an indefinite form and has a "large" semi-simple part (but it can fail to be semi-simple in general).
We prove that this implies that if -dover-bar > 4, one can reconstruct the number of non-backtracking (closed or not) walks through a given edge, the Perron-Frobenius eigenvector of T (modulo a natural symmetry), as well as the closed walks that pass through a given edge in both directions at least once.
Language: | English |
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Publisher: | The Electronic Journal of Combinatorics |
Year: | 2018 |
ISSN: | 10778926 and 10971440 |
Types: | Journal article |
DOI: | 10.37236/5909 |