Questions tagged [regular-graph]

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Chromatic number of regular graphs using spectra

There exist inequalities relating the maximum and minimum eigenvalues of the adjacency matrix of a graph with its chromatic numbers, i.e. the Wilf's and Hoffmann's inequalities, which put together ...
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The diameter of random regular graphs

In 1982, B. Bollobas and Vega in the paper gave the configurational model to generate $r$-regular random graphs. They gave the following theorem (Theorem 1 in the paper). Theorem: Let $r\geq 3$ and $\...