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In a graph $\text{G}$ there is one and only one path between every pair of vertices then $\text{G}$ is a

  1. Path
  2. Walk
  3. Tree
  4. Circuit
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A Graph G(V,E) called as TREE if there is exactly one path between every two vertices.

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Let G be a graph and let there be exactly one path between every pair of vertices in G. So G is connected. Now G has no cycles, because if G contains a cycle, say between vertices u and v, then there are two distinct paths between u and v, which is a contradiction.
Thus G is connected and is without cycles, therefore it is a tree.

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 can u please specify the diagram for understanding. Iā€™m getting a complete graph...thanks in advance

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3 votes
3 votes

ans is (c)

 path in a graph is a finite or infinite sequence of edges which connect a sequence of vertices which, by most definitions, are all distinct from one another. In a directed graph, a directed path (sometimes called dipath[1]) is again a sequence of edges (or arcs) which connect a sequence of vertices, but with the added restriction that the edges all be directed in the same direction.

walk is any route through a graph from vertex to vertex along edges. A walk can end on the same vertex on which it began or on a different vertex. A walk can travel over any edge and any vertex any number of times.

tree is an undirected graph in which any two vertices are connected by exactly one path. In other words, any acyclic connected graph is a tree

circuit is path that begins and ends at the same vertex. Cycle. A circuit that doesn't repeat vertices is called a cycle. A Connected Graph. A graph is said to be connected if any two of its vertices are joined by a path

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@kvkumar.

In a walk, no edge is traversed more than once. But vertex may appear mor than once. So cycle can b part of the walk.

A path is an open walk where no vertex is repeated more than once.

So, why not (A) the answer? And isnt tree a path ?
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2 votes
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Ans C) Tree

Answer:

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