Abstract: A new approach is presented for obtaining closed analytic formulas for the Kirchhoff index for circulant foliations of graphs. The simplest examples of such foliations are circulant graphs. More complex examples include prism graphs, sandwich graphs, discrete tori, and many others. This paper derives explicit analytic formulas for the Kirchhoff index and studies their asymptotic behavior. Results are published in [1, 2]. References [1] A.D. Mednykh, I.A. Mednykh, Cyclic coverings of graphs. Counting rooted spanning forests and trees, Kirchhoff index, and Jacobians, Russian Math. Surveys, (2023), V. 78:3, P. 501–548. [2] Mednykh, A.D., Mednykh, I.A. The Kirchhoff Indices for Circulant Graphs, Sib Math J., (2024). V. 65, P. 1359–1372.

Cite: Mednykh A.D.
Kirchhoff index for circulant foliations of graphs
Probability Techniques in Analysis and Approximation Theory 24-29 Nov 2025