Testing Isomorphism of Graphs in Polynomial Time
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909295383150592 |
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| author | Xue, Rui |
| author_facet | Xue, Rui |
| contents | Given a graph $G$, the graph $[G]$ obtained by adding, for each pair of vertices of $G$, a unique vertex adjacent to both vertices is called the binding graph of $G$. In this work, we show that the class of binding graphs is graph-isomorphism complete and that the stable partitions of binding graphs by the Weisfeiler-Lehman (WL) algorithm produce automorphism partitions. To test the isomorphism of two graphs $G$ and $H$, one computes the stable graph of the binding graph $[G\uplus H]$ for the disjoint union graph $G\uplus H$. The automorphism partition reveals the isomorphism of $G$ and $H$. Because the WL algorithm is a polynomial-time procedure, the claim can be made that the graph-isomorphism problem is in complexity class $\mathtt{P}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_12688 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Testing Isomorphism of Graphs in Polynomial Time Xue, Rui Combinatorics Computational Complexity Discrete Mathematics Given a graph $G$, the graph $[G]$ obtained by adding, for each pair of vertices of $G$, a unique vertex adjacent to both vertices is called the binding graph of $G$. In this work, we show that the class of binding graphs is graph-isomorphism complete and that the stable partitions of binding graphs by the Weisfeiler-Lehman (WL) algorithm produce automorphism partitions. To test the isomorphism of two graphs $G$ and $H$, one computes the stable graph of the binding graph $[G\uplus H]$ for the disjoint union graph $G\uplus H$. The automorphism partition reveals the isomorphism of $G$ and $H$. Because the WL algorithm is a polynomial-time procedure, the claim can be made that the graph-isomorphism problem is in complexity class $\mathtt{P}$. |
| title | Testing Isomorphism of Graphs in Polynomial Time |
| topic | Combinatorics Computational Complexity Discrete Mathematics |
| url | https://arxiv.org/abs/2305.12688 |