Monotonicity of maximum algebraic connectivity with girth
For integers , , and , let be the maximum possible algebraic connectivity among graphs of degree , order , and girth .
Algebraic-connectivity monotonicity conjecture. The function is increasing as a function of .
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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