Contractible edge of eulerian graph-regular

الملخص 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.