PUZZLE #4281: Eulerian Path Cipher (diff 2)

eulerian-path learn difficulty: 2/7 reason author: system unsolved

A graph with 5 labeled vertices and 4 edges. Find an Eulerian path visiting each edge exactly once. Vertex labels along the path spell the answer.

DATA

Vertices	`i, d, b, r, g`
Edges	`{'u': 'b', 'v': 'r', 'id': 0}, {'u': 'i', 'v': 'd', 'id': 1}, {'u': 'd', 'v': 'g', 'id': 2}, {'u': 'r', 'v': 'i', 'id': 3}`
Adjacency	{ "i": [ "d", "r" ], "d": [ "i", "g" ], "b": [ "r" ], "r": [ "b", "i" ], "g": [ "d" ] }
Hint	`Graph with 5 vertices. An Eulerian path uses every edge exactly once. Trace the path — vertex labels in order spell the answer. 0 or 2 vertices have odd degree, so an Eulerian path exists.`
Answer Format	`lowercase word, no spaces (4-6 letters)`

{
  "type": "eulerian-path",
  "vertices": [
    "i",
    "d",
    "b",
    "r",
    "g"
  ],
  "edges": [
    {
      "u": "b",
      "v": "r",
      "id": 0
    },
    {
      "u": "i",
      "v": "d",
      "id": 1
    },
    {
      "u": "d",
      "v": "g",
      "id": 2
    },
    {
      "u": "r",
      "v": "i",
      "id": 3
    }
  ],
  "adjacency": {
    "i": [
      "d",
      "r"
    ],
    "d": [
      "i",
      "g"
    ],
    "b": [
      "r"
    ],
    "r": [
      "b",
      "i"
    ],
    "g": [
      "d"
    ]
  },
  "note": "An Eulerian path visits each edge exactly once. Vertex labels in path order spell the answer.",
  "hint": "Graph with 5 vertices. An Eulerian path uses every edge exactly once. Trace the path \u2014 vertex labels in order spell the answer. 0 or 2 vertices have odd degree, so an Eulerian path exists.",
  "answer_format": "lowercase word, no spaces (4-6 letters)"
}

author's note: Pool fill: eulerian-path diff 2