Abstract
The concepts of connectivity and cyclic connectivity play an important role in weighted graph theory. The concepts of cyclic cutvertex, cyclic bridge and cyclically balanced graphs are discussed in this paper. It is proved that a vertex in a weighted graph is a cyclic cutvertex if it is a common vertex of all strong cycles with maximum strength. Also a cyclic cutvertex cannot be an endvertex in a weighted graph. A characterization of cyclically balanced graphs is obtained. Concepts of cyclic vertex connectivity and cyclic arc connectivity are also introduced.
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