Abstract. Edge degree conditions have been studied since the 1980s, mostly with regard to hamiltonicity of line graphs and the equivalent existence of domi-.

Edge degree conditions have been studied since the 1980s, mostly with regard to hamiltonicity of line graphs and the equivalent existence of dominating ...

Besides hamiltonicity and traceability, there are many studies on the properties of graphs with edge degree conditions, including the characterization of ...

Jul 5, 2014 · Results on the best possible Lai's conditions for Hamiltonian line graphs of 3-edge-connected graphs or 3-edge-connected supereulerian graphs ...

Results on the best possible Lai's conditions for Hamiltonian line graphs of 3-edge ... Degree conditions, Spanning and dominating closed trails, Hamiltonian line ...

Results on the best possible Lai's conditions for Hamiltonian line graphs of 3-edge-connected graphs or 3-edge-connected supereulerian graphs are given, which ...

T is a dominating trail (D-trail) if every edge of G is incident with at least one vertex of T. A circuit is a nontrivial closed trail. Sufficient conditions ...

every edge of the graph if and only if the graph is connected and each vertex has even degree, except that disjoint endvertices u and u have odd degree. Thus,. ...

An example shows that if a graph satisfies the conditions above except that it has too many vertices of degree 2, then the conclusion fails. This result is ...

(ii) An edge is in a closed trail if and only if it is in a cycle. (iii) There is an odd closed walk, if and only if there is an odd cycle. Proof. (i) Let ...