Entries of the bottleneck matrices of maximal outerplanar graphs

In this paper, we consider the entries of the bottleneck matrices of maximal outerplanar graphs. We recall patterns from [Kirkland SJ, Neumann M, Shader BL. Characteristic vertices of weighted trees via Perron values. Linear Multilinear Algebra. 1996;40:311–325.] involving the entries of bottleneck matrices for trees. We first establish similar patterns involving the diagonal entries of bottleneck matrices for maximal outerplanar graphs. We then investigate patterns involving the off-diagonal entries of bottleneck matrices for maximal outerplanar graphs and establish similar results to those found in [Kirkland SJ, Neumann M, Shader BL. Characteristic vertices of weighted trees via Perron values. Linear Multilinear Algebra. 1996;40:311–325.] for trees. We close with examples illustrating our results.