Monotonicity of maximum algebraic connectivity with girth

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For integers dd, nn, and gg, let f(g;d,n)f(g;d,n) be the maximum possible algebraic connectivity among graphs of degree dd, order nn, and girth gg.

Algebraic-connectivity monotonicity conjecture. The function f(g;d,n)f(g;d,n) is increasing as a function of gg.

This is presented as a stronger conjecture motivated by the same computational data on cubic and quartic graphs. It remains an open problem.

References

Primary source

Geoffrey Exoo, Theodore Kolokolnikov, Jeanette Janssen and Timothy Salamon, “Attainable bounds for algebraic connectivity and maximally-connected regular graphs”, arXiv:2307.07308 (2023).

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