What does this research mean for the field?

Balanced bipartite graphs with specific minimum degree and edge-connectivity can be characterized by their maximum adjacency spectral radius, which also provides a condition to ensure a spanning tree packing number of at least k. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

Characterize the extremal spectral radius for balanced bipartite graphs with prescribed edge-connectivity and determine spectral radius conditions for edge-disjoint spanning tree packing.

August 22, 2026Discrete MathematicsOpen Access

Spectral radius, edge connectivity and edge-disjoint spanning tree in bipartite graphs

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Characterize the extremal spectral radius for balanced bipartite graphs with prescribed edge-connectivity and determine spectral radius conditions for edge-disjoint spanning tree packing.
Analyzed the adjacency spectral radius of balanced bipartite graphs relative to their minimum degree and edge-connectivity κ'(G).
Derived spectral bounds to guarantee a minimum spanning tree packing number τ(G) ≥ k.
Identified and characterized the unique extremal graph structures achieving the maximum adjacency spectral radius among all balanced bipartite graphs with given minimum degree and edge-connectivity.
Established a sharp spectral radius condition that guarantees the existence of at least k edge-disjoint spanning trees (τ(G) ≥ k) in balanced bipartite graphs.

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Implication

Graph-theoretic analysis characterizes maximum spectral radius and spanning tree packing in balanced bipartite graphs, highlighting spectral thresholds for network robustness.

Cite This Study

Shi et al. (2026) studied this question.

synapsesocial.com/papers/6a895f53ca7ade938187ddc1 https://doi.org/10.1016/j.disc.2026.115375

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Implication

Graph-theoretic analysis characterizes maximum spectral radius and spanning tree packing in balanced bipartite graphs, highlighting spectral thresholds for network robustness.

Spectral radius, edge connectivity and edge-disjoint spanning tree in bipartite graphs

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Discussion

Implication

Cite This Study

Spectral radius, edge connectivity and edge-disjoint spanning tree in bipartite graphs

Key Points

Discussion

Implication

Cite This Study

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