Bridge and cycle degrees of vertices of graphs. (1984)

• Record Type: Journal Article
• Authors: Chartrand, Gary; Saba, Farrokh; Wormald, Nicholas C.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 7:Number 2(1984)
• Page Start: 351
• Page End: 360
• Publication Date: 1984
• Subjects: bridge degree -- cycle degree -- bridge-cycle degree; Mathematics -- Periodicals; 510.5
• DOI: 10.1155/S0161171284000375
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : The bridge degreebdeg v and cycle degreecdeg v of a vertexv in a graphG are, respectively, the number of bridges and number of cycle edges incident withv inG . A characterization of finite nonempty setsS of nonnegative integers is given for whichS is the set of bridge degrees (cycle degrees) of the vertices of some graph. The bridge-cycle degree of a vertexv in a graphG is the ordered pair( b, c ), wherebdeg v = b andcdeg v = c . Those finite setsS of ordered pairs of nonnegative integers for whichS is the set of bridge-cycle degrees of the vertices of some graph are also characterized.