Bridge and cycle degrees of vertices of graphs
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)...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
1984-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171284000375 |
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| _version_ | 1832545343730876416 |
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| author | Gary Chartrand Farrokh Saba Nicholas C. Wormald |
| author_facet | Gary Chartrand Farrokh Saba Nicholas C. Wormald |
| author_sort | Gary Chartrand |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-f4f114102fdb4a01ad25533f3a894c94 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1984-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-f4f114102fdb4a01ad25533f3a894c942025-02-03T07:26:14ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251984-01-017235136010.1155/S0161171284000375Bridge and cycle degrees of vertices of graphsGary Chartrand0Farrokh Saba1Nicholas C. Wormald2Department of Mathematics, Western Michigan University, Kalamazoo 49008, Michigan, USADepartment of Mathematics, Western Michigan University, Kalamazoo 49008, Michigan, USADepartment of Mathematics, University of Newcastle, AustraliaThe 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.http://dx.doi.org/10.1155/S0161171284000375bridge degreecycle degreebridge-cycle degree. |
| spellingShingle | Gary Chartrand Farrokh Saba Nicholas C. Wormald Bridge and cycle degrees of vertices of graphs International Journal of Mathematics and Mathematical Sciences bridge degree cycle degree bridge-cycle degree. |
| title | Bridge and cycle degrees of vertices of graphs |
| title_full | Bridge and cycle degrees of vertices of graphs |
| title_fullStr | Bridge and cycle degrees of vertices of graphs |
| title_full_unstemmed | Bridge and cycle degrees of vertices of graphs |
| title_short | Bridge and cycle degrees of vertices of graphs |
| title_sort | bridge and cycle degrees of vertices of graphs |
| topic | bridge degree cycle degree bridge-cycle degree. |
| url | http://dx.doi.org/10.1155/S0161171284000375 |
| work_keys_str_mv | AT garychartrand bridgeandcycledegreesofverticesofgraphs AT farrokhsaba bridgeandcycledegreesofverticesofgraphs AT nicholascwormald bridgeandcycledegreesofverticesofgraphs |