图的搜索方法咨询：如何查询特定图信息及类似OEIS的图搜索引擎

Hey there, let's tackle your graph theory search questions clearly and practically:

When you're looking for a specific graph, start with its defining features—this is way more effective than vague searches. Here's what to do:

• Extract core invariants first: Note down key properties like number of vertices, number of edges, regularity (degree of each vertex), whether it's bipartite, Hamiltonian, its girth (length of the shortest cycle), chromatic number, or any unique subgraphs it contains.
• Use precise keyword combinations: Plug these invariants into academic databases or specialized graph directories. For example, if you're looking for a 12-vertex 4-regular graph with no triangles, search for exactly that phrase.
• Leverage graph visualization matching: If you have a drawing of the graph, use tools that support image-based graph matching (many graph theory software packages have this built-in) to cross-reference against known graph libraries.

Let's break this down with your Petersen graph example and the OEIS-like tool question:

确认是否为已知图（比如Petersen图） #

• Match invariants first: For the graph you've found, compute its key invariants. The Petersen graph, for example, has 10 vertices, is 3-regular, has girth 5, diameter 2, and a distinct spectrum (eigenvalues of its adjacency matrix). Cross-reference these with known graph catalogs—if all invariants line up perfectly, it's almost certainly a named classic graph.
• Check canonical forms: Convert your graph's adjacency matrix into a canonical form (a standardized representation that's the same for all isomorphic graphs). Most graph tools can do this automatically, and you can compare this canonical form against entries in graph databases to confirm matches.

类似OEIS的图搜索引擎 #

Yes, there are dedicated tools that work like OEIS but for graphs:

• Invariant-based search tools: These accept inputs like adjacency matrices, sequences of invariants (vertex count, edge count, chromatic number, spectrum, etc.), and match them against a curated database of known graphs. They'll return the graph's name, known properties, and related research if it exists.
• Software-integrated catalogs: Many popular graph theory software packages come with built-in libraries of named graphs. You can input your graph's structure (via adjacency matrix or edge list) and the software will check if it matches any entry in its catalog, often providing instant confirmation and additional details.

内容的提问来源于stack exchange，提问作者Daniel Paleka