Labeling vertices of a polygon in Mathematica

Given a set of points in the plane T={a1,a2,...,an} then Graphics[Polygon[T]] will plot the polygon generated by the points. How can I add labels to the polyg开发者_高级运维on's vertices? Have merely the index as a label would be better then nothing. Any ideas?

pts = {{1, 0}, {0, Sqrt[3]}, {-1, 0}};
Graphics[
 {{LightGray, Polygon[pts]},
  {pts /. {x_, y_} :> Text[Style[{x, y}, Red], {x, y}]}}
 ]

To add point also

pts = {{1, 0}, {0, Sqrt[3]}, {-1, 0}};
Graphics[
 {{LightGray, Polygon[pts]},
  {pts /. {x_, y_} :> Text[Style[{x, y}, Red], {x, y}, {0, -1}]},
  {pts /. {x_, y_} :> {Blue, PointSize[0.02], Point[{x, y}]}}
  }
 ]

update:

Use the index:

pts = {{1, 0}, {0, Sqrt[3]}, {-1, 0}};
Graphics[
 {{LightGray, Polygon[pts]},
  {pts /. {x_, y_} :> 
     Text[Style[Position[pts, {x, y}], Red], {x, y}, {0, -1}]}
  }
 ]

Nasser's version (update) uses pattern matching. This one uses functional programming. MapIndexed gives you both the coordinates and their index without the need for Position to find it.

pts = {{1, 0}, {0, Sqrt[3]}, {-1, 0}};
Graphics[
 {
  {LightGray, Polygon[pts]},
  MapIndexed[Text[Style[#2[[1]], Red], #1, {0, -1}] &, pts]
  }
 ]

or, if you don't like MapIndexed, here's a version with Apply (at level 1, infix notation @@@).

pts = {{1, 0}, {0, Sqrt[3]}, {-1, 0}};
idx = Range[Length[pts]];
Graphics[
 {
  {LightGray, Polygon[pts]},
  Text[Style[#2, Red], #1, {0, -1}] & @@@ ({pts, idx}\[Transpose])
  }
 ]

This can be expanded to arbitrary labels as follows:

pts = {{1, 0}, {0, Sqrt[3]}, {-1, 0}};
idx = {"One", "Two", "Three"};
Graphics[
 {
  {LightGray, Polygon[pts]},
  Text[Style[#2, Red], #1, {0, -1}] & @@@ ({pts, idx}\[Transpose])
  }
 ]

You can leverage the options of GraphPlot for this. Example:

c = RandomReal[1, {3, 2}]
g = GraphPlot[c, VertexLabeling -> True, VertexCoordinateRules -> c];

Graphics[{Polygon@c, g[[1]]}]

This way you can also make use of VertexLabeling -> Tooltip, or VertexRenderingFunction if you want to. If you do not want the edges overlaid, you may add EdgeRenderingFunction -> None to the GraphPlot function. Example:

c = RandomReal[1, {3, 2}]
g = GraphPlot[c, VertexLabeling -> All, VertexCoordinateRules -> c, 
   EdgeRenderingFunction -> None, 
   VertexRenderingFunction -> ({White, EdgeForm[Black], Disk[#, .02], 
       Black, Text[#2, #1]} &)];

Graphics[{Brown, Polygon@c, g[[1]]}]