Abstract
A graph is minimally k-(edge)-connected if it is k-connected (respectively, k-edge-connected) and deleting any arbitrary chosen edge always leaves a graph which is not k-connected (respectively, k-edge-connected). What is the maximum (signless Laplacian) spectral radius and what are the corresponding extremal graphs among minimally k-(edge)-connected graphs for k≥2? Chen and Guo (2019) gave the answer to k=2 and characterized the corresponding extremal graphs. In this paper, we first give the answer to k=3 for minimally 3-connected graphs. For the signless Laplacian spectral radius, we also consider the problem for k=2,3 and characterize the extremal graphs.
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