Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral Bounds for the Connectivity of Regular Graphs with Given Order   The second-largest eigenvalue and second-smallest Laplacian eigenvalue of a
graph are measures of its connectivity. These eigenvalues can be used to
analyze the robustness, resilience, and synchronizability of networks, and are
related to connectivity attributes such as the vertex- and edge-connectivity,
isoperimetric number, and characteristic path length. In this paper, we present
two upper bounds for the second-largest eigenvalues of regular graphs and
multigraphs of a given order which guarantee a desired vertex- or
edge-connectivity. The given bounds are in terms of the order and degree of the
graphs, and hold with equality for infinite families of graphs. These results
answer a question of Mohar.

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The categories of this paper are: stat
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The categories of this paper are: econ
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
37
The categories of this paper are: supr-con