A characterization of generalized cospectrality of rooted graphs with applications in graph reconstruction
Combinatorics
2024-08-06 v1
Abstract
Extending a classic result of Johnson and Newman, this paper provides a matrix characterization for two generalized cospectral graphs with a pair of generalized cospectral vertex-deleted subgraphs. As an application, we present a new condition for the reconstructibility of a graph. In particular, we show that a graph with at least three vertices is reconstructible if there exists a vertex-deleted subgraph that is almost controllable and has a nontrivial automorphism.
Keywords
Cite
@article{arxiv.2408.02488,
title = {A characterization of generalized cospectrality of rooted graphs with applications in graph reconstruction},
author = {Wei Wang and Wenqiang Wen and Songlin Guo},
journal= {arXiv preprint arXiv:2408.02488},
year = {2024}
}
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9 pages