For a connected graph G, a vertex subset F ⊂ V(G) is a cyclic vertex-cut of G if G - F is disconnected and at least two of its components contain cycles. The cardinality of a minimum cyclic vertex-cut of G, denoted by κc(G), is the cyclic vertex-connectivity of G. In this paper, we show that for any integer n ≥ 4, the n-dimensional star graph SGn has κc(SGn) = 6(n - 3).
Strongly conflict-avoiding codes are used in the asynchronous multiple-access collision channel without feedback. The number of codewords in a strongly conflictavoiding code is the number of potential users that can be supported in the system. In this paper, an improved upper bound on the size of strongly conflict-avoiding codes of length n and weight three is obtained. This bound is further shown to be tight for some cases by direct constructions.
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