http://www.bing.com:80/search?q=Isomorphic+Graph+Practice+QuestionsSearch resultshttp://www.bing.com:80/s/a/rsslogo.gifhttp://www.bing.com:80/search?q=Isomorphic+Graph+Practice+QuestionsCopyright © 2026 Microsoft. All rights reserved. These XML results may not be used, reproduced or transmitted in any manner or for any purpose other than rendering Bing results within an RSS aggregator for your personal, non-commercial use. Any other use of these results requires express written permission from Microsoft Corporation. By accessing this web page or using these results in any manner whatsoever, you agree to be bound by the foregoing restrictions.https://math.stackexchange.com/questions/441758/what-does-isomorphic-mean-in-linear-algebraHere an isomorphism just a bijective linear map between linear spaces. Two linear spaces are isomorphic if there exists a linear isomorphism between them.Mon, 13 Apr 2026 07:27:00 GMThttps://math.stackexchange.com/questions/4216211/what-exactly-is-an-isomorphismAn isomorphism picks out certain traits of one object, certain traits of the other, and shows that the two objects are the same in that specific way. Two sets are "isomorphic" when there is a $1-1$ mapping between them, so in this case isomorphism means having the same cardinality--the same number of elements.Thu, 16 Apr 2026 12:17:00 GMThttps://math.stackexchange.com/questions/1549008/what-does-it-mean-when-two-groups-are-isomorphicFor sets: isomorphic means same cardinality, so cardinality is the "classifier". For vector spaces: isomorphic means same dimension, so dimension (i.e., cardinality of a base) is our classifier. I is a bit more complex but still not too difficult (you'll probably encounter it in your book sooner or later) to classify finite abelian groups.Thu, 09 Apr 2026 08:00:00 GMThttps://math.stackexchange.com/questions/731724/what-is-the-difference-between-homomorphism-and-isomorphismBijectivity is a great property, which allows to identify (up to isomorphisms!) the given groups. Moreover, a bijective homomorphism of groups $\varphi$ has inverse $\varphi^ {-1}$ which is automatically a homomorphism, as well. This is a non trivial property, which is shared for example, by bijective linear morphisms of vector spaces over a field. If we consider topology, things change a lot ...Sat, 11 Apr 2026 09:10:00 GMThttps://math.stackexchange.com/questions/421741/what-is-exactly-the-meaning-of-being-isomorphic11 I know that the concept of being isomorphic depends on the category we are working in. So specifically when we are building a theory, like when we define the natural numbers, or the real numbers, or geometry, I often hear that people say that such a structure is complete in the sense that any other set that satisfy their properties is ...Thu, 09 Apr 2026 17:05:00 GMThttps://math.stackexchange.com/questions/5127875/isomorphic-groups-beyond-the-isomorphism-is-this-also-true-for-homomorphismEach isomorphism has an inverse, which is also an isomorphism between the groups. So yes: "being isomorphic" goes beyond the isomorphism in that strict sense. What we mean when we say two things in mathematics, not just group theory, are isomorphic is that the algebraic structure remains the same up to a relabelling of all the constituent parts. Consider, for example, the classical ...Thu, 02 Apr 2026 03:22:00 GMThttps://math.stackexchange.com/questions/24722/what-are-useful-tricks-for-determining-whether-groups-are-isomorphicProving that two groups are isomorphic is a provably hard problem, in the sense that the group isomorphism problem is undecidable. Thus there is literally no general algorithm for proving that two groups are isomorphic. To prove that two finite groups are isomorphic one can of course run through all possible maps between the two, but that's not fun in general. For your particular example ...Sun, 12 Apr 2026 08:04:00 GMThttps://math.stackexchange.com/questions/3141500/are-these-two-graphs-isomorphic-why-why-notAre these two graphs isomorphic? According to Bruce Schneier: "A graph is a network of lines connecting different points. If two graphs are identical except for the names of the points, they are ...Thu, 16 Apr 2026 02:52:00 GMThttps://math.stackexchange.com/questions/2486944/how-to-tell-whether-two-graphs-are-isomorphicUnfortunately, if two graphs have the same Tutte polynomial, that does not guarantee that they are isomorphic. Links See the Wikipedia article on graph isomorphism for more details. Nauty is a computer program which can be used to test if two graphs are isomorphic by finding a canonical labeling of each graph.Wed, 15 Apr 2026 00:01:00 GMThttps://math.stackexchange.com/questions/1650460/whats-an-isomorphismSo all that treating isomorphic objects as equal is completely justified in homotopy type theory. By itself that wouldn't be that exciting, but homotopy type theory is a (fairly minor in some ways) extension of Martin Löf type theory which has been studied by type theorists and computer scientists and implemented for decades.Sun, 12 Apr 2026 23:42:00 GMT