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Neighborhood unions and regularity in graphs
2001
Theoretical Computer Science
One way to generalize the concept of degree in a graph is to consider the neighborhood N (S) of an independent set S instead of a simple vertex. The minimum generalized degree of order t of G is then deÿned, for 16t6 (the independence number of G), by ut = min{|N (S)|: S ⊂ V; S is independent and |S| = t}. The graph G is said to be ut-regular if |N (S1)| = |N (S2)| for every pair S1; S2 of independent sets of t elements, totally ut-regular (resp. totally ut6s-regular where s is given 6 ) if it
doi:10.1016/s0304-3975(00)00246-2
fatcat:anw2upbwgzef7kprzbvgehalbu