A polynomial‐time algorithm for simple undirected graph isomorphism

Abstract

In the author list, "Ferry Sansoto" should be Ferry Susanto.• To reflect more accurately the contribution of the article, the title should be changed to "A permutation and equinumerosity based polynomial-time algorithm for simple undirected graph isomorphism."• In the abstract, the "Pythagorean Triples Theorem" should be removed.• In the abstract, "squared sums of elements" should be "nth power sums."

ISOMORPH: an efficient application on GPU for detecting graph isomorphism

“…From a theoretical point of view, we have found works such as Czajka and Pandurangan (2008), Arvind et al (2012) and He et al (2021), on which this article is based, to efficiently implement this algorithm using the HPC techniques. Other future opportunities are opened from this work, for example, the sub-graph isomorphism, in the beginning also explored from a theoretical point of view, as other authors do in Cordella et al (2004), Konagaya et al (2016), but in the same way, underexplored from an efficiency point of view.…”

“…In He et al (2019) and later in He et al (2022), Jing He et al describe an algorithm of simple undirected graph isomorphism. This algorithm uses the vertexes and edges adjacency matrix representation to prove that two graphs are isomorphic.…”

“…It is known that if two graphs are isomorphic then their vertexes adjacency is similar. Jing He et al prove that the array of row sum for both vertexes adjacency and edges adjacency matrix of a graph is a permutation of another if and only if G ' H. Thus, the algorithm described in He et al (2022) provides us with a great method to determine if an isomorphism exists between two graphs.…”

“…In 3, steps are defined as follows:Step 1Step 2Step 3: Implement the singular vector composition (SVD) on both vertex and edge adjacency matrices for two graphs. Check if the corresponding eigenvalue is equinumerous (He et al ., 2022). Step 4: Check if the maximum linearly independent system of the left and right singular vector of both vertex and edge adjacency matrices isomorphic (He et al ., 2022).…”

“…Check if the corresponding eigenvalue is equinumerous (He et al ., 2022). Step 4: Check if the maximum linearly independent system of the left and right singular vector of both vertex and edge adjacency matrices isomorphic (He et al ., 2022). …”