Geodesic
A characterization of generalized cospectrality of rooted graphs with applications in graph reconstruction
Wei Wang1 ; Wenqiang Wen2 ; Songlin Guo3
1Tarim University
2Anhui Polytechnic University
3Wanjiang University of Technology
The electronic journal of combinatorics, Tome 32 (2025) no. 4
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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. Namely, if a vertex-deleted subgraph $G-v$ of $G$ is almost controllable, then the graph $G$ is reconstructible if $G-v$ either has a nontrivial automorphism group, or is asymmetric with a specific property.
DOI : 10.37236/13610
Classification : 05C50, 05C60
Mots-clés : reconstructible graphs, almost controllable vertex-deleted subgraph

Wei Wang  1   ; Wenqiang Wen  2   ; Songlin Guo  3

1 Tarim University
2 Anhui Polytechnic University
3 Wanjiang University of Technology 
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     author = {Wei Wang and Wenqiang  Wen and Songlin Guo},
     title = {A characterization of generalized cospectrality of rooted graphs with applications in graph reconstruction},
     journal = {The electronic journal of combinatorics},
     year = {2025},
     volume = {32},
     number = {4},
     doi = {10.37236/13610},
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Wei Wang; Wenqiang  Wen; Songlin Guo. A characterization of generalized cospectrality of rooted graphs with applications in graph reconstruction. The electronic journal of combinatorics, Tome 32 (2025) no. 4. doi: 10.37236/13610

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