The structure of (t, r)-regular graphs of large order

The structure of (t, r)-regular graphs of large order,10.1016/S0012-365X(03)00200-0,Discrete Mathematics,Robert E. Jamison,Peter D. Johnson Jr.

The structure of (t, r)-regular graphs of large order   (Citations: 1)
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A graph is (t,r)-regular iff it has at least one independent t-set of vertices and the open neighborhood of any such set contains exactly r vertices. Our goal is to show that when t⩾3 and the order is sufficiently large, then the structure of (t,r)-regular graphs is similar to, but not exactly the same as the structure of (2,r)-regular graphs as derived by Faudree and Knisley. That is, there is an “almost” complete kernel of order at most r surrounded by satellite cliques, all of the same order, which are “mostly” joined to the kernel.
Journal: Discrete Mathematics - DM , vol. 272, no. 2-3, pp. 297-300, 2003
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    • ...G is uniformly (t,r)-regular if 1 t n and for each S V (G) with |S| = t, |NG(S)| = r. This property of graphs was introduced in [4] as “(t,r)-regularity”; the problem with that terminology is that it is also used for a seemingly similar but rather less exigent property, introduced in [3] and written on in [2], [5], and [7]...

    Dean Homanet al. There Are No Non-Trivially Uniformly (t,r)Regular Graphs for t> 2

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