I'd like to delete a github branch using a GraphQL mutation, but I haven't found enough information regarding the deleteRef command. Using the GraphQL explorer I came up with this nonsense:
mutation {
  deleteRef(input: {refId: "my-branch"}) {
    __typename
  }
}
I don't know yet how to add repository information for the mutation to have any meaning, and the only reason I included __typename was because the deleteRef block couldn't be left empty. How do I fix this mutation?
You can't return nothing in that mutation since it's not of type Void. You need to define a mutation like the following : 
mutation DeleteBranch($branchRef: ID!) {
  deleteRef(input: {refId: $branchRef}) {
    __typename
    clientMutationId
  }
}
In the explorer you can define queries and mutations and choose which one to execute when you hit the button. A full example in the explorer would be :
query GetBranchID {
  repository(name: "test-repo", owner: "bertrandmartel") {
    refs(refPrefix: "refs/heads/", first: 100) {
      nodes {
        id
        name
      }
    }
  }
}
mutation DeleteBranch($branchRef: ID!) {
  deleteRef(input: {refId: $branchRef}) {
    __typename
    clientMutationId
  }
}
with variables:
{
  "branchRef": "MDM6UmVmMjQ5MDU0NzQ0Om1hc3Rlcg=="
}
You can do the following in the explorer :
GetBranchID querybranchRef variableDeleteBranchWithout the explorer, here's how it would look using python :
import requests
repo_name = "YOUR_REPO"
repo_owner = "YOUR_USERNAME"
token = "YOUR_TOKEN"
query = """
query {
  repository(name: \"""" + repo_name + """\", owner: \"""" + repo_owner + """\") {
    refs(refPrefix: "refs/heads/", first: 100) {
      nodes {
        id
        name
      }
    }
  }
}
"""
resp = requests.post('https://api.github.com/graphql', 
    json={ "query": query},
    headers= {"Authorization": f"Token {token}"}
)
body = resp.json()
for i in body["data"]["repository"]["refs"]["nodes"]:
    print(i["name"], i["id"])
chosenBranchId = input("Enter a branch ID: ")
query = """
mutation {
  deleteRef(input: {refId: \"""" + chosenBranchId + """\"}) {
    __typename
    clientMutationId
  }
}
"""
resp = requests.post('https://api.github.com/graphql', 
    json={ "query": query},
    headers= {"Authorization": f"Token {token}"}
)
print(resp.json())
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