"Cayley's formula" meaning in English

{
  "etymology_text": "Named in honour of Arthur Cayley.",
  "forms": [
    {
      "form": "Cayley's theorem",
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      "name": "en-noun"
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
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          "kind": "other",
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          "source": "w"
        }
      ],
      "glosses": [
        "A formula for the number of spanning trees of a complete graph of n vertices: nⁿ⁻²."
      ],
      "id": "en-Cayley's_formula-en-noun-Lb5cf8dV",
      "links": [
        [
          "graph theory",
          "graph theory"
        ],
        [
          "spanning trees",
          "spanning trees"
        ],
        [
          "complete graph",
          "complete graph"
        ]
      ],
      "raw_glosses": [
        "(graph theory) A formula for the number of spanning trees of a complete graph of n vertices: nⁿ⁻²."
      ],
      "tags": [
        "uncountable"
      ],
      "topics": [
        "graph-theory",
        "mathematics",
        "sciences"
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      "wikipedia": [
        "Arthur Cayley",
        "Cayley's formula"
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    }
  ],
  "word": "Cayley's formula"
}

{
  "etymology_text": "Named in honour of Arthur Cayley.",
  "forms": [
    {
      "form": "Cayley's theorem",
      "tags": [
        "canonical"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "-",
        "head": "Cayley's theorem"
      },
      "expansion": "Cayley's theorem (uncountable)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
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        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
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        "English uncountable nouns",
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        "en:Graph theory"
      ],
      "glosses": [
        "A formula for the number of spanning trees of a complete graph of n vertices: nⁿ⁻²."
      ],
      "links": [
        [
          "graph theory",
          "graph theory"
        ],
        [
          "spanning trees",
          "spanning trees"
        ],
        [
          "complete graph",
          "complete graph"
        ]
      ],
      "raw_glosses": [
        "(graph theory) A formula for the number of spanning trees of a complete graph of n vertices: nⁿ⁻²."
      ],
      "tags": [
        "uncountable"
      ],
      "topics": [
        "graph-theory",
        "mathematics",
        "sciences"
      ],
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      ]
    }
  ],
  "word": "Cayley's formula"
}