International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 2, Pages 351-360
Bridge and cycle degrees of vertices of graphs
1Department of Mathematics, Western Michigan University, Kalamazoo 49008, Michigan, USA
2Department of Mathematics, University of Newcastle, Australia
Received 2 February 1982
Copyright © 1984 Gary Chartrand et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The bridge degree and cycle degree of a vertex in a graph are, respectively, the number of bridges and number of cycle edges incident with in . A characterization of finite nonempty sets of nonnegative integers is given for which is the set of bridge degrees (cycle degrees) of the vertices of some graph. The bridge-cycle degree of a vertex in a graph is the ordered pair , where and . Those finite sets of ordered pairs of nonnegative integers for which is the set of bridge-cycle degrees of the vertices of some graph are also characterized.