COMPUTER SCIENCE AND ENGINEERING
DATA STRUCTURES
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Question
[CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
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an undirected graph with no cycles
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a directed graph with no cycle
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an undirected graph with cycles
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a directed graph with cycle
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Detailed explanation-1: -A tree is an undirected graph G that satisfies any of the following equivalent conditions: G is connected and acyclic (contains no cycles). G is acyclic, and a simple cycle is formed if any edge is added to G. G is connected, but would become disconnected if any single edge is removed from G.
Detailed explanation-2: -A tree is a connected graph with no cycles. A forest is a graph with each connected component a tree. A leaf in a tree is any vertex of degree 1.
Detailed explanation-3: -A connected acyclic graph is called a tree. In other words, a connected graph with no cycles is called a tree. The edges of a tree are known as branches.
Detailed explanation-4: -Definition: A tree is a connected graph without any cycles, or a tree is a connected acyclic graph. The edges of a tree are called branches. It follows immediately from the definition that a tree has to be a simple graph (because self-loops and parallel edges both form cycles).
Detailed explanation-5: -A graph without cycles is called an acyclic graph.