Oct 24, 2017 · A more general approach to graph isomorphism is to look for graph invariants: properties of one graph that may or may not be true for another. (The degree sequence of a graph is one graph invariant, but there are many others.) This is usually a quick way to prove that two graphs are not isomorphic, but will not tell us much if they are. For ...

Aug 16, 2012 · Graph Isomorphism Query: Analyzing Two Graphs for Isomorphism and Proving Non-Existence of Vertex Isomorphism Hot Network Questions Is it a good idea to wrap node.js package functions in a micro-service architecture?

Dec 9, 2024 · Such an f is called an isomorphism of the graphs G and G′. While the definition seems to consider the set of vertices instead of labels, I’m confused because many textbook and internet examples express graph isomorphism as a map from labels to labels just like the below picture from Wikipedia.

Jun 22, 2015 · In addition to the above-mentioned definition of a graph invariant, I would like to point out that, according to some authors, a graph invariant may be something different from a number; for example, according to Gross and Yellen (Graph Theory and its Applications, Second Edition, CRC, Boca Raton, 2006, page 89), "a graph invariant is a property of graphs that is …

BTW, your 2. is an excerpt from Wikipedia entry Graph Automorphism, if you'd have bothered to read the next sentence you would see: "...That is, it is a graph isomorphism from G to itself." $\endgroup$

Nov 11, 2020 · A graph morphism is a pair of maps between the respective ... Directed graph isomorphism condition ...

Aug 27, 2017 · In practice, graph isomorphism can be tested efficiently in many instances by Brendan McKay's NAUTY program. There was a question about the workings of the NAUTY algorithm previously on this site, and one of the comments (by user gilleain) linked to this explanation of McKay's Canonical Graph Labeling Algorithm.

In other words, proofs of NP-completeness seem to require a certain amount of redundancy in the target problem, a redundancy that GRAPH ISOMORPHISM lacks. Unfortunately, this lack of redundancy does not seem to be much of a help in designing a polynomial time algorithm for GRAPH ISOMORPHISM either, so perhaps it belongs to NPI.

Jun 1, 2020 · I have one question about the algorithm on testing the Trivalent Graph isomorphism in polynomial time. The paper "Isomorphism of graphs of bounded valence can be tested in polynomial time" by Luks was complicated to me. As I understood, given 2 Trivalent Graphs, we can test whether they are isomorphism in polynomial time.

Feb 13, 2018 · Two connected 2-regular graphs with countable infinite many vertices are always isomorphic. This graph is called double-ray. There is a model of random graphs on a countable infinite set of vertices such that every such graph is isomorphic to any other. This graph is called the Rado graph.