International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 2, Pages 351-360
doi:10.1155/S0161171284000375
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.
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.