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Generating asymmetric keys as a tree graph in a deterministic way using a seed value requires the use of a hierarchical deterministic key (HD key) generation algorithm. The HD key generation algorithm generates a master key from a seed value, which can then be used to derive a hierarchy of child keys.

Here are the general steps to generate asymmetric keys as a tree graph in a deterministic way using a seed value:

Choose a cryptographic hash function, such as SHA-256, and a seed value. The seed value should be a cryptographically secure random value.
Use the seed value to generate a master private key using the HD key generation algorithm. This master private key will be the root of the tree graph.
Use the master private key to derive a master public key.
For each child node in the tree graph, use a unique identifier, such as an index number, to generate a child private key from the master private key using the HD key generation algorithm.
Use the child private key to derive a child public key.
Repeat steps 4 and 5 for each level of the tree graph, deriving child keys from their parent keys.
The resulting tree graph will have the master public key at the root, with child public keys at each level branching out to child nodes. Each node in the tree graph will have a corresponding private key that can be used to sign or decrypt data.

It's important to note that the specific implementation of the HD key generation algorithm will depend on the cryptographic library being used. However, most modern libraries, such as OpenSSL or libsodium, provide APIs for HD key generation that can be used to implement the above steps.

The hierarchical deterministic key (HD key) generation algorithm can be used with the elliptic curve secp256k1, which is commonly used in blockchain applications, as well as other cryptographic applications. There are several HD key generation algorithms that can be used with secp256k1, but one of the most popular is the BIP32 algorithm, which is defined by the Bitcoin Improvement Proposal 32.

The BIP32 algorithm is based on the secp256k1 elliptic curve, and it uses a combination of hash functions and elliptic curve arithmetic to generate a hierarchy of child keys from a master key. Here are the general steps for generating an HD key hierarchy with the BIP32 algorithm:

Choose a cryptographically secure seed value, which can be a random number or a passphrase.
Use a hash function, such as SHA-256, to generate a 512-bit master key from the seed value.
Split the 512-bit master key into two 256-bit values, known as the private key and chain code.
Use the private key to generate a public key, which can be used to derive child keys.
Use the chain code and private key to derive a hardened child key at a given index in the hierarchy.
Use the public key and chain code to derive a non-hardened child key at a given index in the hierarchy.
Repeat steps 5 and 6 to generate a hierarchy of child keys.
Note that the BIP32 algorithm can be extended to support different elliptic curves, including secp256k1. To use secp256k1 with the BIP32 algorithm, you'll need to modify the algorithm to use the appropriate elliptic curve parameters for secp256k1. This can typically be done using a library that supports secp256k1, such as libsodium or OpenSSL.

There are several libraries available for Java and TypeScript that implement the BIP32 algorithm for hierarchical deterministic key (HD key) generation. Here are a few options:

For Java:

bitcoinj: A popular Bitcoin library for Java that includes support for BIP32 HD key generation.
Bouncy Castle: A cryptographic library for Java that includes support for BIP32 HD key generation, as well as other cryptographic functions.
Trezorj: A lightweight Bitcoin library for Java that includes support for BIP32 HD key generation and works with hardware wallets like Trezor.
For TypeScript/JavaScript:

bitcoin-ts: A TypeScript library for Bitcoin development that includes support for BIP32 HD key generation.
hdkey: A JavaScript library for HD key generation that supports BIP32 and other HD key generation algorithms.
bip32-utils: A JavaScript utility library for working with BIP32 HD keys, including key derivation and serialization.
Note that while these libraries support the BIP32 algorithm for HD key generation, they may have differences in implementation and syntax. It's important to carefully review the documentation and examples for each library to ensure that it meets your specific needs.