If the graph start and end with same vertex and no other vertex can be repeated then it is called trivial graph.
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No.
A cycle is a closed path such that the end vertex of the final edge is the start vertex of the first edge.
Look at Einstein's theory on gravity. It is shown on a parabolic graft.
Simply, updating the existing distance with later received minimal value when a shortest path problem is solved in a graph. K.M.Anura Wijayasingha.
A tree in which one vertex called the root, is distinguished from all the others is called a rooted tree.