Bridge and cycle degrees of vertices of graphs

Gary Chartrand, Farrokh Saba and Nicholas C. Wormald

International Journal of Mathematics and Mathematical Sciences, 1984, vol. 7, 1-10

Abstract:

The bridge degree bdeg v and cycle degree cdeg v of a vertex v in a graph G are, respectively, the number of bridges and number of cycle edges incident with v in G . A characterization of finite nonempty sets S of nonnegative integers is given for which S is the set of bridge degrees (cycle degrees) of the vertices of some graph. The bridge-cycle degree of a vertex v in a graph G is the ordered pair ( b , c ) , where bdeg v = b and cdeg v = c . Those finite sets S of ordered pairs of nonnegative integers for which S is the set of bridge-cycle degrees of the vertices of some graph are also characterized.

Date: 1984
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:465164

DOI: 10.1155/S0161171284000375

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