graphql, how to design input type when there are "add" and "update" mutation?

A very common pattern is to have separate input types for each mutation. You may also want to create one mutation query per operation. Perhaps something like this:

const typeDefs = `
  input AddBookInput {
    title: String!
    author: String!
  }

  input UpdateBookInput {
    # NOTE: all fields are optional for the update input 
    title: String
    author: String
  }

  type Book {
    id: ID!
    title: String!
    author: String!
  }

  type Query {
    books: [Book!]!
  }

  type Mutation{
    addBook(input: AddBookInput!): Book
    updateBook(id: String!, input: UpdateBookInput!): Book
  }
`;

Some people also like to include the update ID as part of the update input:

const typeDefs = `
  input AddBookInput {
    title: String!
    author: String!
  }

  input UpdateBookInput {
    # NOTE: all fields, except the 'id' (the selector), are optional for the update input 
    id: String!
    title: String
    author: String
  }

  type Book {
    id: ID!
    title: String!
    author: String!
  }

  type Query {
    books: [Book!]!
  }

  type Mutation{
    addBook(input: AddBookInput!): Book
    updateBook(input: UpdateBookInput!): Book
  }
`;

Finally, you may want to use a 'payload' type for the return type - for added flexibility (gives you more wiggle room to change the return type later without breaking your API):

const typeDefs = `
  input AddBookInput {
    title: String!
    author: String!
  }

  input UpdateBookInput {
    # NOTE: all fields, except the 'id' (the selector), are optional for the update input 
    id: String!
    title: String
    author: String
  }

  type Book {
    id: ID!
    title: String!
    author: String!
  }

  type AddBookPayload {
    book: Book!
  }

  type UpdateBookPayload {
    book: Book!
  }

  type Query {
    books: [Book!]!
  }

  type Mutation{
    addBook(input: AddBookInput!): AddBookPayload!
    updateBook(input: UpdateBookInput!): UpdateBookPayload!
  }
`;

Hope this helps!