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math.CO2026
The Distance Spectrum Does Not Determine Bipartiteness
Feifan Gong, Kehua Wang, Wei Wang
Over a decade ago, Koolen, Hayat, and Iqbal posed the problem of whether the distance spectrum determines bipartiteness within the class of connected graphs. In this paper, we reso…
math.CO2026
A Family of Simultaneously Cospectral Trees for Degree-Distance Matrices
Limeng Lin, Quanyu Tang, Kehua Wang +1
Spectral characterization of graphs for various graph matrices constitutes a central topic in spectral graph theory. Let be a graph with adjacency matrix , diagonal degre…
math.CO2026
On the Spectral Determination of Complements of \(T\)-shape Trees
Feifan Gong, Kehua Wang, Wei Wang
A graph \(G\) is said to be \emph{determined by its spectrum} if every graph cospectral with \(G\) is isomorphic to \(G\). A \emph{T-shape tree} is defined as a tree containing exa…