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Contractible edge of eulerian graph-regular
Author
Source
Issue
Vol. 11, Issue 4 (31 Dec. 2016), pp.15-29, 15 p.
Publisher
University of Thi-Qar Research and Development Department
Publication Date
2016-12-31
Country of Publication
Iraq
No. of Pages
15
Main Subjects
Topics
Abstract EN
In this paper define the contractible edge eulerian graph that, let μ is a class of Eulerian graphs G∈μ, the edge e in G is called contractible edge eulerian graph if G*e∈μ.
The necessary conditions for Eulerian graphs to have contractible edge eulerian have been introduced, further, the even and odd contractible edge eulerian graph have been studied , we also define the contractible edge eulerian graph class, the edge e in G is satisfied property contraction is called contractible edge eulerian if G*e∈μ.
Tutte [7] proved every 3-connected graph non isomorphic to k_4 have 3-contractible and proved every 3-connected graph on more than four vertices contains an edge whose contraction yield a new 3-connected graph [7].
We proved graph G is eulerian graph has contractible edge if non isomorphic to k_4.
How over every 4-connected graph on at least seven vertices can be reduced to smaller 4-connected graph by contraction one or two edge subsequently [7].
Also we discussed the graph G is eulerian on at least seven vertices can be contraction and saved the properties of eulerian graph.
Let G be a regular graph and eulerian graph, the edges e in G is called contractible regular-eulerian graph if G*e is regular-eulerian grah, We discussed relation contraction of eulerian-regular graph then G has contractible if d(v)=2, if d(v)>2 then G has not contractible regular-eulerian.
American Psychological Association (APA)
Sanjur, Azhar Aziz. 2016. Contractible edge of eulerian graph-regular. University of Thi-Qar Journal،Vol. 11, no. 4, pp.15-29.
https://search.emarefa.net/detail/BIM-779302
Modern Language Association (MLA)
Sanjur, Azhar Aziz. Contractible edge of eulerian graph-regular. University of Thi-Qar Journal Vol. 11, no. 4 (Dec. 2016), pp.15-29.
https://search.emarefa.net/detail/BIM-779302
American Medical Association (AMA)
Sanjur, Azhar Aziz. Contractible edge of eulerian graph-regular. University of Thi-Qar Journal. 2016. Vol. 11, no. 4, pp.15-29.
https://search.emarefa.net/detail/BIM-779302
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 29
Record ID
BIM-779302