Abstract
In this paper, a D-closed trail problem for a class of the graph G under condition of constraint is discussed. We prove line graph L(G) of G is a Hamiltonian graph by using the method of induced sub-graph’s degree analysis. The main result of this paper is that let G be a simple connected, almost bridgeless graph of order n≥3,G≠K 1,n − 1, Q 1 and Q 2, if d(I)≥2n-6 for each induced sub-graph I isomorphic to P 4, then, G has a D-closed trail. Accordingly, line graph L(G) of G is a Hamiltonian graph.
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